How about no 'Third Treaty of San Ildefonso', so Louisiana territory remains split between Britain and Spain, with the Spanish bit later becoming part of Mexico? Maybe the British part would join in the rebellion though (or be so sparsely populated/garrisoned that it wouldn't matter), if not the Americans would probably try to invade it à la Canada.
If the Spanish bit becomes part of Mexico, it'll go faster than you can say "Me-who?" The President Jefferson, an avowed Franco-phile, was prepared to form a military alliance with
Britain to fight
France for the port city, and Britain generally favored/allowed any US interest that kept the US's views away from Canada. Mexico, which couldn't even control its own lands and distinctly lacked a naval tradition needed to maintain forces so far away, would be distinctly at a disadvantage.
I've written a few long posts on the topic of the US's need for New Orleans, but it can simply be put that the US needed unlimited/guaranteed right of deposit in New Orleans for its west-of-appalachians lands (which were considerable even then), and even Jefferson made New Orleans the immediate Grand Strategy of the young United States; the Louisiana Purchase was intended for the port only, not the entire territory (even though that was near-useless without the port).
Any power who holds New Orleans that holds the US will likely see the US seek British acceptance/aid/alliance in order to take the port. Any power who is allied with Britain may easily see the US try, especially in the case of Spain where it already has enough troubles with Florida and the rest of its empire. The only power who the US might absolutely not attack would be Britain, except that (a) the US proved that it would attack less than a decade later, (b) New Orleans doesn't serve British interests in the area but is a cost to defend, and (c) holding New Orleans is likely to spur more conflict with the US, not less. Which is bad from the British point of view as it costs money to defend lands from a nation who would otherwise be a big trading partner. (That it would also be bad from the US PoV if it failed is irrelevant; we know that the US
would attack Britain (1812), and US interests are secondary to British interests).