Interesting question.
It'd probably have to be the Spanish and they were running out of Spaniards already for their vast empire so you'd most likely get an extension of the mission system used in the rest of North America and some plantations, managed out of Cuba (the admin center for Spanish "Lousiana".) Thinly held and populated I think we'd see a repeat of American immigrants into Texas extending slaveholding and eventually rebelling, whether it was eventually Mexican or remained Spanish-controlled...the Filibusters were already lusting after it and considering it when Napoleon sold it off (the new biography of General James Wilkinson talks about that as he was the Army officer trying to head that off while on the payroll of both the Spanish and French as well as conspiring with Aaron Burr's filibustering scheme for a Louisiana kingdom.)
If Napoleon didn't send that large army to Haiti first where they died off to disease as they were to go to New Orleans after crushing the sugar slaves' rebellion in Haiti...putting a veteran French army in New Orleans that was larger and better than the entire American army would have been a huge change. Assume they're trapped in New Orleans/St. Louis by the ebb and flow of the Napoleonic wars keeping the French fleet elsewhere. The French did vastly better with the Native American tribes than the British, Americans, or Spanish so forming military alliances the length and breadth of the Mississippi Valley with the tribes would be certain and arming them with French arms and French advisors (like in the 3 French & Indian Wars a few decades earlier), might have worked in trapping the American expansion to roughly the Appalachian mountains with feuding over the connecting Ohio River Valley as happened OTL. Intermarriage of the French troops with Native wives: Choctaw, Creek, Illinoi, Wabash, Osage, Pawnee/Arikara, etc. would again be certain and create a Metis population (like Manitoba, Canada in the 19th century) firmly rooted and now networked with a major power for supply and strategy. Whether it would pose a threat to Canada along the Great Lakes by attack from French troops and Indian proxy armies up from the Mississippi would be a logistical stretch but force the British to put more troops and money into Canadian defense which would weaken Britain's European continent forces a bit (probably using Canadian Ojibwe and Cree/Metis already tied to the Hudson's Bay and Northwest Fur Companies' as proxy armies there would be the British strategy as well, just as in the War of 1812 on the Mississippi where they took Chicago and Detroit that way and were headed for St. Louis to complete link up with Pakenham's assumed conquest of New Orleans.)
A French Metis nation controlling the Mississippi River Valley's length well into or throughout the 19th century would butterfly a lot:
1. Would the loss of so much "free land" severely reduce the immigration to the U.S. (or divert it to Canada, Argentina, Mexico, etc. to a greater degree than OTL?)
2. New Orleans became the primary port of the South for cotton exporting so losing it and the rich plantation lands of Mississippi, Louisana, etc. would constrain the growth and value of Southern slavery, maybe avoid the Civil War entirely (given Jefferson Davis, Abraham Lincoln, Henry Clay, Andrew Jackson, and many more either come from or came to prominence from places that would now be French Metis is whole string of major butterflies in the timeline as well.
3. France's control of Spain during the Napoleonic era would make the fuzzy border of Lousiana and Northern Mexico (California, Wyoming, Colorado etc.) either not a point of friction or formally ceded over to the French by Napoleon's brother, who ran Spain at the moment...much of that's reached by the Missouri River and St. Louis as well so quite possible.
4. Developing French industry along the Mississippi and Missouri for eventual cities rather than just a network of trading forts/villages would be possible in the early 19th century as well. St. Louis had major iron and lead mines within a couple of decades OTL and Illinois surface deposits of coal and lead were being mined by the 1850's OTL so French Kansas City, Des Moines, Chicago, Minneapolis, Council Bluffs would be quite possible given the French traders out of St. Louis established many of them OTL and worked out the overland trade route West, the Santa Fe Trail, in a decade or two of this OTL. Frenchmen had a really lousy deal back home for centuries, emigrating from there to the rich farmland and temperate climates of the Mississippi Valley, as opposed to Northern Canada or hot jungle hells below the Equator, might well have drawn vastly more, especially after the fall of Napoleon (unless this somehow helps him survive.)
5. With this to absorb the French for a century, it's dubious or inevitable that the Prince Maximilian/French Army conquest of Mexico in the 1860's would occur, which would have all sorts of major impacts in Mexican history, particularly no rise of Porfiro Diaz from the Mexican resistance to run Mexico for 30+ years, the Mexican Revolutions against Diaz and his successors, and the fossilizing of that party into control of Mexico almost to today so huge butterflies there (and Mexico would likely have a far less tragic history.)