My idea:
Sometime in the 1720's, some French governor realizes how well-suited the lower Mississippi is for cash-crop agriculture (sugar, indigo, and rice in the south, cotton on the Mississippi Delta) and convinces the French government back in Paris to seriously invest in the place. From the 1720's to the 1750's, France brings in, say, 30,000 settlers (I understand the OTL number was around 7,000, so I don't think this is a huge stretch. And not all of them would be French), plus twice as many slaves (some from Haiti and their other Caribbean islands, some straight from Africa). They settle the lower Mississippi river-OTL Louisiana and Mississippi, plus small parts of Tennessee and Arkansas.
After the Seven Years War, Lower Louisiana, all the way to the Appalachains, is ceded to Spain, with Britain taking Illinois and the Ohio valley. Spain, however, doesn't attempt to assimilate the French planter aristocracy, instead being content simply to tax them. Louisiana gets a modest amount of immigration during the Spanish period, but they tend to assimilate into the already-resident French population.
The American Revolution and Napoleon happen as OTL, but meanwhile, Spain tries to ban American settlers from *Tennessee and *Alabama. As French settlement is mostly concentrated along the Mississippi, these territories are largely unpopulated and thus the ban is virtually impossible to enforce. Spanish attempts at it, however, manage (after being highly sensationalized in American news reports) to infuriate the public of the nascent US, and in a series of escalating diplomatic incidents, Spain closes New Orleans and its part of the Mississippi to American shipping. Meanwhile, the Napoleonic Wars are going on right now with France and Spain allied against Britain. America jumps in on the British side, and in the ensuing war expels the Spanish from Louisiana with British help.
Under American rule, Louisiana recieves a goodly amount of Anglophone settlers, and cities like New Orleans and Baton Rouge become bilingual. The Francophones, for their part, are uneasy at coming under American rule, but the once they're admitted as a state, their state constitution establishes French and English as co-official languages and guarantees protection for the Catholic church.
Nevertheless, the French planter aristocracy remains quietly resentful at rule from the "foreigners" in Washington, and, along with South Carolina, become one of the most anti-federalist, pro-states rights places in the US. This gradually gets mixed up into the South's general antagonism towards the free states of the North (much of the Francophone elite own slaves, and don't like Anglo, Protestant Abolitionists lecturing them about what grave sinners they are, and the animosity is mutual). Manifest destiny still exists ITTL, and the *Mexican War and *ACW still happen, with Louisiana supporting the *Confederacy. The *Civil War and the cotton bust of the late 19th century contribute to Louisiana's becoming a rather economically backward place, with the same civil rights problems as the rest of the south, and the addition of a highly influential Catholic church. In the 1960's century, this leads to a large civil rights movement, which takes on nationalistic overtones (a large majority of the black people are Francophone), eventually leading to an active secessionist movement.
Thoughts?