If you are looking at "what if", this is before Jackson has kicked all the southern Indians out of Georgia, Alabama and Mississippi. Creeks, Choctaws, Chickasaws, Cherokees and Seminoles. Presumably a number of these would ally with the French to stop the onrushing settlers. Perhaps some would stick with the US and others stay neitral.
This presumes Jefferson would get into a fight, declared or otherwise. He didn't have an sterling record as governor of Virginia during the Revolution. He did go along with reducing the Army to some 3,200 troops (2 infantry, 1 artillery regiment) and disbanded the Commissary Corps, leaving supplies to civilian contractors who were found badly wanting during the War of 1812. He did write soaring prose. And purchased Louisiana when the chance arose.