Sounds like a British wet dream: the damn Frogs and uppity Colonials kicking the snot out of one another.
As for the war if the Brits stay neutral between the two belligerents I'd expect:
A. Naval war goes in favor of the French, as OTL: "During the course of the fighting, the new US Navy captured 85 French privateers, while losing approximately 2,000 merchant vessels." - About.com (if trustworthy!

)
B. The US quickly invades and likely seizes Louisiana (at least initially).
C. Land war...hmmm. France is already fighting a losing battle in Haiti, demanding lots of troops. Plus the fight with Britain. A lot depends on if France can spare the troops. If she can, expect 1812 analog with US invaded, cities torched. The US has (plus side) a cadre of ARW veterans (not as available or spry in 1812) and surviving blooded officers, but (minus side) is broke, in debt, and has no real standing army of note any more. Also, considering southern Francophilia, this could divide the nation at a critical phase.
D. The real fight is over New Orleans, or whether the US can keep it if France sends a serious expeditionary force to retake it. Expect Creek and possibly Choctaw and Chickasaw uprisings and inter-tribal wars. It will get ugly quickly.
Synopsis: All in all, not a good thing for either side. The US is young, poor, and weak. France is recovering from the horrors of revolution, losing her crown colony in Haiti, and fighting the British. Neither side is likely to come out well.
Winner: Britain.
Loser: US
and France.