Tell me if any of this is just too crazy:
With some selective meddling in the early 1600s (it is a challenge; we don't have to be anal about plausibility) much of the civil and religious strife that France suffered in that period can be avoided. That'lll go a long way: the Huegenots can stay in France and not aid Britain, L'Etat will be better off financially, and France will generally have a freer hand.
Obviously the two biggest long-term problems for France are England and Germany, the former for its pesky world empire and navy driving it to power and the latter for the fact that, if it were united, it would inevitably vie with France for hegemony over Europe.
England, I think, can be dealt with fairly easily-they are due for a civil war. IIRC one of Tony Jones' TLs had a less popular Cromwell regime which in turn leads to a violent monarchist return, which in turn leads to a repressive, backwards Britain. Or, if we want to go back a bit farther, we could have the Spanish Armada have better luck (Drake's attack fails, clear skies all the way to England). England becomes a rather troublesome Spanish fief; even the obstinate Spanish Habsburgs, I think will let go eventually. So maybe sometime in the 1640s or 1650s some pretender or other gains foreign support and drives the Spanish out. England will be weak for quite a while; notably, they'll probably have to build a navy basically from scratch, and they won't even be able to think of colonization for a while. If we want to go over the top, maybe we can have the French and English somehow get into a tussle quickly, ending with a succesful French invasion. Combine that with some extra focus on the New World by an alt-Louis Xsomething (maybe sending some dregs of society over), and I think we might see a New World divided between the French, Dutch and maybe Swedish.
Germany is a bit harder-the trick is to keep nationalism from becoming the overpowering force it did in OTL. A good place to start with that would be having the Thirty Year's War be either butterflied away or drastically shortened, as it was one of the major causes of modern German nationalism. Prussia should be crushed somewhere along its insanely fortuitous rise to power. If a situation can be set up where, with limited German nationalism, there's no one power strong enough to dominate Germany (the Austrians being focused on holding their multinational empire together), I think France is set for long-term hegemony in Western Europe.
So, I'm thinking that by the 1730s England is a quiet little island (quite probably without Ireland or Scotland) with no pretensions at power, the HRE is the mess its always been with a lot more French influence, Italy is disunited but remains a battleground between the French and Austrians, and Spain is in its Inevitable Decline (I'm being sarcastic-I know full well how uninevitable Spain's decline was; unfortunately, powerful Spain doesn't mesh well with super-France), and Russia is a rising power in the East. France is set for quite a while.