France as a medieval kingdom occupied much the same area as classical Gaul, but having prospered under the Pax Romana its people spoke Latin, and having been invaded by the Franks its blood was no longer Celtic.
The lands had become part of a great empire under the rule of Charlemagne, but after his death in 814 the empire was split into three parts and his son Charles the Bald took control of the western portion. Having had a father known as Charles the Magnificent, Charles the Bald tried to improve his epithet with an an attempt to reunite the empire. This failed. Charles the Fat had even more motivation but his attempt to reunite the empire also failed.
The Carolingian line eventually died out in the western kingdom, which was probably just as well given the number of bald and fat people it turned out. The leading nobles then elected a new king, Hugh Capet and thus the Capetian dynasty was born. France was by now a generally feudal kingdom, and the Capetians had to work long and hard at politics in order to build their authority. This was not least because the crown itself held little land, and accordingly the king relied on persuading some of the nobles to support him when he had disputes with other nobles. And usually the only way to do this was to reward them in some way, from resources already slim. One of their most difficult land holders was Henry II, King of England. As you can imagine, getting him to swear fealty was a difficult task. No least because, when Louis VII divorced Eleanor of Aquitaine (who held about a fifth of the country in her own right as her father's heir), she then married Henry and he (and his sons, Henry the Young King, Richard, and John after him) took over her lands, and added them to the links with the Duchy of Normandy and with the Norman kingdoms in Italy.
The Capetian line was replaced by the Valois dynasty. Their hobbies included losing to the English at Agincourt, not saving Joan of Arc from the English and slaughtering Protestants on St Bartholemew's day. They were replaced by the Bourbons in 1589, who were even worse and so the French gave up on monarchy all together in the late eighteenth century.
France was one of the earliest countries to progress from feudalism to the nation-state. Its monarchs surrounded themselves with capable ministers, and French armies were among the most innovative, disciplined, and professional of their day.