Personally, I don't think France is "broken" per se. I'm fine when France is a major European power and is able to defeat everyone of his many enemies in a 1vs1 situation. But I do think that there are some things that definitely need to be changed/worked on.
First, France is to easily unified. French lands are rich and have a large base manpower, and when France unites his core lands, it becomes extremely strong. In general, that is no problem, but as it stands, France usually kicks everyones ass around 1500, when it has absorbed/conquered all of the French OPM's. That makes France ahistoricly strong. I'm fine when France is the dominant power in Europe Mid- to Lategame, but this shouldn't be the case this early. I would suggest to give all the French minors national traditions to protect them from early integration. Either give them the Hungarian/Berber tradition which gives +200% coring cost, or give them a tradition that slows down the integration process itself (I think this would be best idea).
My second concern are coalitions. Others have already pointed out how they are flawed (members of a coalition won't work together properly, they don't make use of their superior numbers, etc.) so I won't go into detail. Simply improve the coalition A.I. I think it got better in the latest patch, I still consider it "broken". One thing that has to be addressed is England/Great Britain. I have NEVER seen them take any action, even if they have provinces bordering France. They just sit in London with their 20k stack and wait. That is especially annoying when England is the war leader of the coalition because it gives a lot less warscore when a province is occupied by an ally of the war leader instead of the war leader itself.
The last problem with the whole matter is the lucky nations mechanic. The small boni to revolt risk, war exhaustion, leaders, etc. are fine, but lucky nations almost always get 6/6/6 rulers. Now that almost every actions in game uses monarch points, which are only generated by the monarch's stats, this makes France (and every other lucky nations) ridiculously powerful. France is rich and powerful, with a big and competent army, but giving them godlike rulers makes them better in almost any aspect of the game, most notably technology. France almost always unlocks techs as soon as they cost 999 MP or less and it has a shitload of ideas. Also, the fact that players can't ever be lucky completely unbalances the whole region. When France is neighbored by Spain, Austria, Burgundy and England, which are all lucky, they tend to be rather docile and even gets wiped out quite some times. But when one of this nations is player by a human player, France has a decisive advantage. Therefore I believe the true problem to be lucky nations.
These are the things that really need a rework, not France itself. The only thing about France that could(!) be changed is the rate of their moral/manpower recovery. France has vast armies, but even if you defeat them, after a few months they reappear with full manpower and moral. Though that is probably in line with history.