This is a list of characters I have done some basic research on for canon relationships, originally for Zodion, but now mostly for personal reference. This is by no means the complete list of canon relationships he has, nor is it a complete picture of each relationship. It is just an overview of some of the most important relationships in his canon.
If you have more information you'd like to toss my way I'd be happy to look it over!
America
Francis has an extremely complicated relationship with America. At first France and England found America as a baby nation and fought over him in what are dubbed as the "French and Indian Wars" (King William's War, Queen Anne's War, King George's War, and finally, the Seven Years War), England inevitably winning the fight and claiming America as his colony in 1763. Then France and the young America, still a colony of England, became friends solely because France wanted to get back at England. He did this by helping America's side during the Revolutionary War. Then, as soon as America became its own country, France almost immediately was launched into his own Revolution. He thought America would help him, but alas, America refused, leading him to simultaneously fight a civil war while being at war with six other kingdoms (the Kingdom of Sardinia, an Italian state; the Kingdoms of Prussia and Spain; the Austrian and Russian empires; and the recently-formed United Kingdom of Great Britain and Ireland), all practically on his own. Napoleon gained massive amounts of territory in the United States in their war with Spain, but Napoleon believed after slave revolts in many Caribbean countries (which were previous French colonies), that he could not stabilize a North American empire. Therefore he was willing to sell the territory for $15 million to keep it out of English hands (in what is referred to as the Louisiana Purchase). America doubled in size overnight, with no warfare involved. One of the major reasons America grew so quickly was because of the fact France was opposed to all of Britain's plans to limit growth in the territory (particularly with expansion into California). Ten years after the hundredth year anniversary of America's independence, France gifted to him the Statue of Liberty, or as it was called back then, Liberty Enlightening the World; in its original French, La Liberté éclairant le monde.
During the First World War, France finally received much-needed enforcements in the last year of the war. The reparations France demanded of Germany after the war were considered ridiculous by most of the allied countries (namely Italy and Japan, who refused to have anything to do with France's demands, and America and England, who tried to talk him out of it). It was the interwar period that saw much harmony among the US and France; American citizens were drawn to France for his theater, art, philosophy, literature, cuisine, and many other things, while the French absolutely adored a new style of music called "jazz" that Americans - namely, African Americans - had created. During the second World War America supported him with supplies but never troops, until the Japanese bombed Pearl Harbor. Now, both administrations are trying to be friendly. While he has disagreed with America's policies quite often in the past (as any American can tell you), he has come to realize that America is a strong nation and that, especially during World War One and World War Two, he needs America's help quite often, particularly against the strong opponent of Germany. Of course he still thinks America's ideas are stupid and blatantly tells him so, but considering this brash, hot-headed, 235-year-old nation has 2600 more nuclear bombs than any of the other countries on Earth and is practically running the global economy, were it not for Germany and Russia and China? Francis is going to stick by America's side, no matter how annoying he finds him.
Canada
Canada is France's dearest former colony, meaning that he treats Canada like a son. Because he IS France's son, in France's mind: they "have the same beautiful hair" according to the anime. France first settled Canada mostly for furs and other natural resources, meeting with the native populations and intermingling with them. Then, he heard of a strange little boy that looked a lot like him, and lived in the woods. He searched out this little boy, and began teaching him his ways - the French language, French culture, everything. He wanted to raise his son Canada correctly, the French way, as all European countries wanted to do at the time (a little something called Imperialism)... but England put a stop to it by stealing Canada away from his rival France in 1759. France was crushed due to being forced to leave his child behind, but as Canada grew up, Canada refused to let France disappear from his life. He sent diplomats to France, regardless of all the legal restrictions England put on its new colony expressly forbidding a political affiliation with France; even up until 1912, the still French-speaking part of Canada (after a hundred years of British rule and only thirty of French rule, I might add) was sending representatives to France.
Then, during the first World War, they officially became allies, because Canada was still England's colony and France and England were now allies. During World War II, France was easily defeated by the Nazis because they had not had time to economically recover from the first World War. However, Canada fought bravely to free his father from Germany's rule. While most Western powers denounced the Vichy regime upon its creation in 1940, Canada still maintained political contact with the Vichy government until 1942, then joining the Free French Forces (best known as the French Resistance) to reclaim France for the Allied Powers. Since then France has been possessive of Canada's "originally French" identity, causing much tension in the nation by catering to the specifically French part of Canada (namely Quebec) and ignoring some of the other provinces. Being only 144 years old (according to himself), Canada still gets babied by France quite often, regardless of actually being a grown nation. France is one of the few people that can "see" him (as he often gets forgotten by other Western powers) and immediately doesn't mistake him for America (with America being the only other person who can do this). France will often go on rants about his "beloved son" to those who will listen.
England
Early, early in their history, France and England once were both ruled by Roman Empire, lovingly referred to by France and Italy as "Grandpa Rome". Then, the Germanic tribes took over and England and France practically had nothing to do with each other. However, in the 1000's, England and France once got along. Surprisingly well, actually. When France was in control of England, they live quite happily together. Even though England always tried to tease France about having long hair and girly clothes, he still always tried to follow in France's footsteps, being younger than him by a hundred years or so. But soon, England realized that France didn't have to control him, and forcibly became his own nation under Richard the Lionheart. This is truly when I believe their relationship to have turned sour, for France had never felt such the sting of abandonment before; he had been fighting the other countries around him (namely, the Holy Roman Empire) but he had never fought with England.
France and England soon launched themselves into the Hundred Years War, which started as a simply a war over territory but soon became a war based on political alliances of their states and the unification as a people - namely, the concept of Nationalism, before it was really defined. France then met Joan of Arc and was instantly smitten with her; not only was she beautiful but she was fighting as a man solely for his sake. England was angered that he was losing to a girl, let alone a human girl, and when she was captured by the Burgundians he immediately bought Joan from them. France, who had fallen deeply in love with Joan at this point, was devastated that she was being burnt at the stake like a common heretic, and started hating England more than seeing him as a rival as he'd done for the past hundred years; Wikipedia sums it up quite nicely by saying, "Apart from setting national identities, the Hundred Years' War is often cited as the root of the traditional rivalry and at times hatred between the two countries." France expelled England out of his territory quite brutally and crushed the Burgundians, and even made a treaty with Scotland (England's brother) against England.
Their history was rife with conflict afterwards, both fighting against each other in the Italian Wars, then in religious wars when England created a new church named after himself (which eventually became the Protestant church), and then in territorial wars when Spain first started losing its status as a colonial power. Both the War of Spanish Succession and the War of Austrian Succession saw them leaping into the conflict to support once side or the other, solely for the purpose of defeating each other (in the War of Austrian Succession, when France pulled out of the war, England was quite soon to follow, leaving the Austrian forces without substantial reinforcements). Even during the colonial period, France and England were racing for territorial control, even going so far as to subdivide India into the "French" part and the "English" part.
But England would not stand for this and swept many of France's colonies out from under his feet, causing further hatred for the other nation to swell by effectively kidnapping what France believed were his children (America and Canada being two of them). France fought England not only during the American Revolution but also during his own Revolution. Napoleon had effectively rebuilt the French state from the ground up and thus France loved him dearly, like a brother. The third and final thing that France really begrudges England for in their history is exiling his beloved emperor, Napoleon, after the destruction of the French empire, onto an island that was extremely poor for the man's health - many English Parliament members as well as many of the newspapers of the time claimed that the British government put him on the island of Saint Helena in order to speed up his death. England, out of spite, kept the two apart until Napoleon died in 1821.
Surprisingly, after the accession of Napoleon III (Napoleon Bonaparte's nephew) to the throne of France in 1848, and a few years previous of cold political policies, the two began to cooperate in a couple of wars together, most notably the Second Opium War against China, being given a part of China to colonize as compensation for their help. After Napoleon III was overthrown the newly-formed French Republic still had a favorable relationship with England namely due to the also newly-formed German Empire which they both believed was a serious threat. Finally, on the 8th of April in 1904, France and England signed the Entente cordiale, and became political allies officially. This is what caused French and English involvement in World War I in the first place, along with the Franco-Russian alliance on August 17, 1892, and the Anglo-Russian Entente on August 31, 1907, when Russia leapt headfirst into the war in support of Serbia and against the Austro-Hungarian empire (all three of them later being known as the Triple Entente).
They fought together and both worked to keep Germany weak so that such a war wouldn't happen again, however, France exacerbated Germany's condition by demanding 132 billion Marks in reparations which England did not believe was possible. France and England found themselves again entering a World War together after the invasion of Poland, and fighting together again as allies, namely the French Resistance and the English armed forces. Even with the shadow of the short-lived Vichy government hanging over France, England still demanded that France have a portion of Allied-occupied Germany in the aftermath of World War II. Once again during the Suez Crisis in 1956 they fought together, but France had been bankrupted so badly by the world wars and the German occupation that he was afraid he would die. So, he proposed to England. As in, marriage proposal. England turned him down outright. Thankfully France managed to avoid the economic crisis he was dreading, under President de Gaulle, and soon created the European Union with what was then West Germany. England was not allowed to join at first, but was allowed to in 1973. In recent years, both the French president and the England parliament have been attempting to forge stronger relations between both countries, and therefore France and England have been doing the same, getting into occasional arguments but still remaining friends.
Germany
France and Germany (who, when he was little, was dubbed the Holy Roman Empire) have been rivals ever since the Treaty of Verdun in 843. In the Treaty, the kingdom of Francis was split into three parts - West, Middle, and East Francia. West Francia became France's territory; East Francia became the Holy Roman Empire's territory as well as Austria's territory; and Middle Francis split up about thirty years later in 870 into a north and south half, the north of which was split up among East and West Francia; this area of the globe would become a long-standing contention between the two nations in the many years to come, roughly corresponding to Alsace and Lorraine (Elsass and Lothringen) later on in history. In fact, the Lorraine and Alsace territories were so much a spot of contention between the two countries that it was not uncommon for the territory thirty years later to belong to the other country from a treaty settlement. The last time the territories switched hands was in the aftermath of World War Two, when France demanded the territory in reparations from the newly-defeated Third Reich; both territories belong to France since the present day.
But going back in time a bit to the Holy Roman Empire: as Austria grew to be a stronger political power, so did the Holy Roman Empire, being an amalgamation of many small German states that were allied with Austria. While France fought constantly against Austria for one reason or another, he ended up fighting with the Holy Roman Empire too, not only for control of territories in Italy but also to suppress the looming German threat to his west. While he did fight numerous wars with Austria over the four hundred years of the Austro-Hungarian empire, they were sporadically placed, as he was more concerned with Holy Roman territory (not only because it actually bordered him but it also held much fertile land on the banks of the Rhine river). The only war they fought in together on the same side during the years of the Holy Roman Empire was in the Crusades, which were short-lived as the Holy Roman Emperor drowned while bathing in a river in the Ottoman Empire.
During the Napoleonic era, Napoleon easily defeated the Holy Roman Empire and dissolved it as a state. It then became known as the Confederation of the Rhine as a German territory under France's control, which he abused quite well, practically wrecking the Rhinish economy until Austria and Prussia both agreed to step in to rescue the German territory (like they both were) from the Latin territory of France. France was forced to cede over the territory to the other German nations of Prussia and Austria in 1815 to create the German Confederation. As Austria and Prussia began fighting over the lands, it soon became the German Confederation in 1866 with Prussia unifying with his brother's lands. Holy Rome was finally reborn as the German Empire in 1871, which made him "grow up" by Nation standards, making him more like the Germany appearing in the show and webcomic. German power began growing and the other nations in Europe new it, creating secretive political alliances that were one of the main causes of the first World War.
In the first World War, France was one of Germany's first targets, right after Belgium. Therefore France and England and Russia all began fighting against Germany due to the Triple Entente, and the fact that Russia was allied with Serbia, who had been accused of assassinating Austria-Hungary's leader. Regardless, France was Germany's closest enemy and was seen as easy to defeat by the German Empire. France was about to lose Paris to the Germans, but in a week from the 5th to the 12th of September in 1914, that was later called the "Miracle of the Marne", he was able to repel the German army (with a bit of England's help) and keep them locked in a trench warfare stalemate for the duration of the war... by using taxi cabs. I kid you not. After the Germans surrendered in 1918, France asked the impossible - 132 billion Deutsch Marks (then $31.4 billion, in 2011 worth $442 billion) in reparations, which would have taken 70 YEARS to pay off. Germany was forced to sign the agreement or else risk being occupied by the Allied Powers. When Germany nearly became bankrupt within the first year of the agreement, he told France he could not continue to make payments. Utterly incensed, France went so far as to invade the Ruhr region of Germany, which held all the factories and was a major economic sector of Germany at the time, to force all workers to work to pay off the debt. Passive resistance of the workers was met by the slaughter of 130 million German civilians by the French army in the two years. Germany's anger for France grew and grew, until he simply ignored the Versailles treaty completely and began to promote sympathy in America and England, finally convincing them to make France back down and sign the Dawes treaty, reducing the Versailles debt by more than 50% by 1929.
It was in 1934 that Adolf Hitler came into power and began the "economic miracle" that put Germany back on top of the world. As payback for France's treatment of him in the decade since the war, Germany invaded Poland in September of 1939, France and England's common ally. France and England both declared war on Germany shortly after, this time unfortunately without Russia's help. France soon found his entire country occupied by Germany, who began to treat him as poorly as France had in the decades previous, creating the Vichy regime in the South. France, in response, created the Free French Forces to keep fighting; even within the Vichy regime there was a network of spies placed that were eventually responsible for the sweeping Allied victory throughout the region in the later years of the war. The second World War ended with Germany (now "West Germany") being split from his brother Prussia (now "East Germany"), with England, America, and France occupying different zones of West Germany and the German capital of Berlin in East Germany.
With the Soviet Bloc becoming at threat to the immediate east of West Germany, he began trying to reintegrate into Western Europe, turning to his neighbor France for assistance. Their relationship grew slowly in the next decade, until finally in 1963 the Élysée Treaty was signed, which laid out a plan for Franco-German cooperation in all areas - politics, economics, culture, and military. West Germany and France were responsible for the creation of the European Union which is still very powerful today, as well as being members of the UN together, and the G6 (now the G8). Overall, their relationship is much closer than in their past, and France is very grateful for Germany as a friend, but he still can't help but be instinctively afraid of Germany because of just how powerful of an enemy he had been in their past.
Italy (North)
Italy was with Germany (HRE) and France in the Roman Empire, but as the Roman Empire began to fall to the Germanic tribes, Rome one day took North Italy and disappeared, leaving France alone and forcing him to become the "adult". France still has many deep-rooted insecurities about this, mostly about the fact he was not "good" enough for Rome, and thus tried to prove his worth by taking much of Italian Renaissance culture and perfecting it to make it specifically French. Opera, ballet, fencing, painting and sculpting - all really started as art forms in Italy. The Italian food culture was mimicked by France and now France is considered the best in the culinary arts around the globe. France loves his brother but he still begrudges him, inwardly, for being the only one to be with Rome when he died; France still isn't quite sure what happened to Rome, because North Italy doesn't remember.
Ever since the Treaty of Verdun, many countries have wanted to claim the south portion of Middle Francia (which roughly corresponds to North Italy) for themselves; one of these countries was France. Seeing as he was Italy's brother, he fought quite often with Austria and the Holy Roman Empire over portions of North Italy's territory, while North Italy was sort of kicked around between those three and Spain. France fought in the Italian Wars for control of the region; therefore he is the one responsible for "killing" Italy's love interest at the time, Holy Roman Empire, who was reborn as Germany without Italy's or Germany's knowledge. Italy fought for freedom from German (namely, Austrian) control in three different instances, finally succeeding in 1870. Italy and France fought together in World War One, and once again in the Allied intervention in the Russian Civil War. They fought against each other in World War II until the year 1943, when Italy defected to the Allies. Since then the Italians and the French have cooperated much like the Germans - economically, culturally, and politically. Francis adores his little brother, only ever calling him "oblivious" when England tries to get France to spread bad rumors about North Italy.
Prussia & Spain
While these two countries are both extremely different in their relationship with France, it is important that these three be spoken about as a group; these three are commonly paired up in wars together, whether on the same side or not, as these three countries were three of the most powerful nations on the European continent. What is most important is that although they have fought against each other in numerous wars, they still remain friends according to Himaruya. Two of the three have ganged up on the other in wars before in history: France and Spain against Prussia in the War of Spanish Succession, Spain and Prussia against France in the War of the Sixth Coalition, and so on and so forth. There have also been many times the three countries have fought together on the same side, such as the War of Austrian Succession and the Patriotic War of 1812. While these three appear to be bitter enemies, they can still cooperate and be friends just as easily. The main point of conflict between the two that has sort of split them apart was during World War II when they were all fighting on a different side - Prussia being forced to fight with Germany, France fighting with the Allies, and Spain fighting to stay neutral. However, political relations with both Germany (which Prussia ceded over his East Germany lands to his little brother after the fall of the Berlin Wall, making him no longer a country by technicality) and Spain have been greatly improving since then.
Turkey
While their relationship is much, much more recent than many of the others on this list, France and Turkey have as much a complicated past as many of the others. The first relations these two countries shared was during the Crusades period, when many Catholic countries allied together to fight the Muslim powers in the regions of Turkey and the Middle East. France and the Ottoman Empire were deeply embroiled in these wars until the Crusades finally ended in 1291. France then began mostly dealing with issues closer to home, most notably the Holy Roman Empire, ignoring the Ottoman Empire for the most part. France and Turkey have been very strong economic allies ever since the Ottoman Empire rose to a dominant position in Europe in the early 1500's, which lasted for more than two and a half centuries, until Napoleon's campaign in Egypt starting in 1798.
They found themselves technically fighting against each other in World War One, as the Ottoman Empire allied with the German Empire, but France was much more occupied with Germany than with the Ottomans during the war; even in the French troops invested in the region during the Gallipoli campaigns, the British and Australian/New Zealand forces were much stronger. They found themselves fighting again in the year 1920 in the aftermath of World War One, which is arguably the most heated war they were involved in together. It was after this that France ended the Cilisia War with a treaty recognizing the new government based in Ankara, which in 1923 became the Republic of Turkey after many other countries recognized this government as the heir to the Ottoman Empire.
Since then, while they have agreed politically on many points, there is the matter of admittance to the EU; France's current president, Nicolas Sarkozy, refuses to let Turkey into the United Nations because of religious differences, and because of the current issue on the island of Cyprus with relation to the Turkish Republic of Northern Cyprus, which is only recognized as a country in Turkey itself. Regardless of this, France and Turkey have both been interested in expanding and promoting each other's cultures in their own countries.