Anyone can pull out a victory if the other side behaves like idiots. The British defeated the preponderance of US forces on land, New Orleans was post-Ghent and served to give the USA a crutch to disguise how weak it really was. Here France can not just raise its own armies, it can finance Indian tribes to raise Hell with nifty new modern firearms......
I don't see how Ghent matters, because neither side knew about it. Similarly, are there any tribes in the region who could be major French allies?
Also, unlike the War of 1812, a Franco-American War would be universally popular. The New England states are traditionally pro-British, after all, and for the South and West New Orleans is essential.