Fix-Its
The Shadow of the Moon Won't Do, by brilligspoons. Slash, Charles/Erik. (ca. 1,200 words)
This is a straightforward alternative to the beach scene, but a lovely example of this genre.
Possible Worlds, by trailingoff. Slash, Charles/Erik. (ca. 12,000 words)
This is a fix-it via a mutant-ex-machina do-over, or rather it takes even more than one try, and I like that they have to work to make things right.
A Family Portrait In Progress, by Xris. Slash, Charles/Erik. (ca. 47,700 words)
This is not so much a direct fix-it as a later reconciliation, in which Charles ended up raising Lorna initially without knowing she's Erik's daughter. It's a series with two finished stories so far.
Enigma, by Yahtzee. Slash, Charles/Erik. (ca. 11,100 words)
Erik goes back in time, but the turning point here is not Cuba but he goes back to before his mother died, becomes a WWII mutant hero, "Enigma", and changes his life as well as history of human-mutant relations.
Undone, by Yahtzee. Slash, Charles/Erik. (ca. 6,600 words)
Another time travel scenario. Here Charles consciousness from post-X3 goes back to his younger self just after Shaw's attack on the CIA.
other AUs
your head caught in a waking dream, by addandsubstract. Slash, Charles/Erik. (ca. 23,100 words)
One that I recced as WIP on the kink meme that has been finished now for a while, so in case you haven't read it yet I thought I'd link again: The scenario here is that Charles' parents had him committed to a mental hospital, which did not help much with his telepathy. Eventually Raven (whom he met like in canon) manages to break him out with Erik's help, and they hunt for Shaw.
Peregrine, by aeshna_uk. Slash, Charles/Erik. (ca. 6,700 words)
This is wingfic, with a winged Erik. This has lovely detail, and I liked that Erik still has his regular powers too.
Night Fishing at the Seine, by furius. Slash, Charles/Erik. WIP
Charles and Erik meet in Paris before the events of XMFC. I'm enjoying the atmosphere of this, and so far am intrigued by the plot.
Tessellation, by nekosmuse. Slash, Charles/Erik. (ca. 116,700 words)
In this AU both Erik and Charles are mutant rights activists. Erik is based in Genosha, and more militant than Charles, but he sort of has a crush on Charles whose writings inspired him. They meet at an event and things between them proceed from there, along with a good action-adventure plot.
MCIS: First Case, by Pookaseraph. Gen. (ca. 25,000 words)
This a modern AU, a fusion with NCIS I suppose, which I don't know, but I read it as just an government mutant agents AU. Erik is an agent, Moira his boss, and she partners Charles with him. The author says it's the first in a series that will be Charles/Erik, but this first is gen.
Taken By His Majesty, by Pookaseraph. Slash, Charles/Erik. (ca. 27,500 words)
Erik is a Roman legionnaire taken captive in Britain by the Celtic leader, Charles.
The Weight of Water, by pprfaith. Het and slash, Charles/Raven, Charles/Raven/Erik. (ca. 51,000 words)
This isn't too far from canon in the setup, except that Charles forms telepathic bonds, and the consequences of that are really well explored here, not just as romance ploy, but also the scary implications, both of Charles being powerful and subtle effects which accumulate and change all three of them.
Limited Release, rageprufrock. Slash, Charles/Erik, Hank/Alex. (ca. 58,000 words)
Another one I've recced before, but now it's finished finished and posted on the AO3, so it's worth pointing out again. It's a loose fusion with White Collar in which Erik is a mutant in the FBI and Alex is a mutant criminal, released to help him hunt for Shaw. It doesn't try to match up with the White Collar scenario completely, but has good worldbuilding and fun plot.
Imaginary Life Journey, by renata_kedavra. Gen, with implied Erik/Raven, Charles/Erik. (ca. 9,000 words)
Two scenarios in which Erik and Raven, and Erik and Charles respectively, try to recruit Kurt Wagner. This just has a lovely atmosphere (and the bits in French and German actually add to that and work), and is a good character study contrasting Kurt and Erik.
Mr. Xavier's Neighborhood, by SharpestScalpel. Slash, Charles/Erik. WIP
This is a series of snippets is adorable. Erik is raising Pietro and Wanda and has a crush on Mr. Xavier who hosts a mutant-tolerance children's show.
New Beautiful Things Come, by singlecrow. Slash, Charles/Erik. (ca. 17,600 words)
This is a modern AU with mutants being public in which Erik has a kosher bakery. It wasn't a setup I expected to get into, but the atmosphere and worldbuilding works, and it's a happy making story.
Linger by waldorph. Slash, Charles/Erik. (ca. 29,700 words)
This is also a modern AU with mutants being public, in which Erik hears Charles in the apartment he rents, like a ghost haunting it. I liked the ensemble plot in this.