Isn't the War of 1812 IOTL?
I doubt the Americans could distract the British sufficiently.
If they were to do strikingly well, they
would demand the attentions of more of the Army, which would need more of the Navy to escort them across, and they
might get stuck there when the French fleet has a spot of good weather. But that's a
lot of conditionals.
Then again, there was some American teenager the other day talking about having the Continental Congress spend its money on a fleet of impossible battleships in the AWI.
If they did something along those lines afterwards that
could tie up the RN. And we can even get some use out of the poor old French officers who fled the Revolution, by giving them new commands. If I'm honest, though, I'm a bit (well, a lot) unsure about this plan, too . . .