The Origins Of France
The Origins Of France, Edward James, ISBN 0-333-27052-5
This book covers the second half of the first millenium CE. At the start of this interval, Gaul was politically fragmented; it had relatively recently ceased to be a Roman province, and it was predominantly populated by Gallo-Romans, Bretons, Franks, Goths and Burgundians.
At the kings-and-battles level the story is one of endless struggle for advantage among the Frankish aristorcracy, culminating in the Carolingian Empire and its subsequent disintegration, with government - such as it was - essentially local by the 10th century. The penultimate chapter is entitled “The Fragmentation Of Gaul”; one might be forgiven for thinking that not much progress had been made, but (as the introduction cautions) that assumes a particular viewpoint, in which the history of a country is the history of its centralization.
Much else changed in this time. Latin had ceased to be generally comprehensible by the 8th century. Identities changed, with the various populations becoming more integrated. The Church grew not only in independence but also the breadth and depth of its influence, for instance taking an increased interest in rural areas and supplanting secular officials in the royal administration - perhaps more by default than by design, and even under protest.
While this is a relatively dense book it is also concise at just over 200 pages excluding back matter, and with an occasional lightheartedness, e.g. a reference to 1066 And All That in the introduction. Of interest not only regarding the narrow question of early France but the more general one of transition from post-Roman to mediaeval.