The only thing is ensuring the immigration is Catholic or Latin/Francophone. Perhaps refocus Irish immigration to New Orleans? Maybe have the British try and vacate French Canada like they did the Arcadians?
Well, the population of francophone New Orleans is strong enough to hold as it did until at least 1920 otl (which isn't extinguished yet, some areas of the metro have very high percentages) while being subject to the melting pot of the US. The francophone population of middle Louisiana such as Aveyolles is strong as well, perhaps the center of rural créole population as opposed to the urban créole population in Nouvelle-Orléans. Acadiana of course was strongly francophone until 1950s. Acadiana is the state of francophone that this Louisiane needs; a population of rural non English speakers who are both religiously opposed to protestant innovations and thus unlikely to interact with them (mimic Québec), this can even be seen in the civil war with generals such as Albert Mouton being afraid to join the army as he was scared of English speakers. Northern areas such as Northern Louisiana such as Shreveport, Ouachita and Bossier where only 20% or so francophone in 1850 or so and thus the beginning of the weakness of this area; which was an acute lack of a large rural population and immigration from the urbanized south such as Nouvelle-Orléans. The issue only gets worse the farther north you go as the percentages are nearly disappeared in the 1840s at the latest, with Arkansea losing its francophone population in at least 1820, Missouri perhaps in the 1840s in terms of absolute percentages and Michigan before then. Other areas west of Saint-Louis and Chicago are essentially uninhabited by Europeans.
Again, the biggest issue, is that urban centers of Louisiane where heavily populated and huge compared to its rural areas. Nouvelle-Orléans for instance was easily 45-55% of the population of Louisiane in 1860, which is the beginning of issues. A large urban center that attracts trade and also is religiously tolerant will always lean to bilingualism which then if not strong enough, leads to monolingualism for the language most conducive to trade. Thus, the imperative is after NO is adequate size, divert all the new immigrants to the north perhaps through lands grants, which would likely be what an independent Louisiane would do to begin with. My propositions for this said state:
1. Haitian rebellion goes as planned and those migrants arrive and cause the huge boom in NO, which for a fe wyears amounted to upwards of 200-300% growths in populations, the vast majority of which were either francophone Europeans or African slaves from Haiti and Sainte-Dominique. This population is perhaps the one that should expand into the countryside as opposed to later migrations. The reason for this is that perhaps if the northern areas are saturated in francophone peoples, these areas will become more and more uninteresting to America to the east and NO will be smaller and less prosperous for the Americans to actively take a shot at. However, the other way could also be true, make NO a massive trade center and population spot attracting more migrants and then through some grant system spread these peoples all over Missouri, Arkansea, Kansas, etc...
2. Have a similar revolt as Haiti but in places like Colombia, Cuba and Venezuela which turn out to be very deadly and large amounts of refugees begin appearing in the Caribbean. Areas like Venezuela had serious connections with Louisiane in this era as well, through the examples of Louisianan pirate such as Jean Laffite and Renato Beluche. These immigrants, could then be attracted to NO by its Catholic faith and wanted due to the need for settlers. These groups then could be spread out all over the northern areas and further bolstering NO's growing population, which will begin at this point in the 1820s (as otl) attracting young french intellectuals who otl would oddly frequent the city in their youth and then return and make a career in France. There needs to be a way to keep and sustain these types of people from France, perhaps as an independent nation as opposed to USA, will make it more attractive for actual residence for extended periods.
3. One thing I feel we all are missing is that there is a possibility of a move of Québécois into the northern sections of Louisiane which already have strong cultural affinity with the so called Muskrat and Missouri French populations of the northern US (the Québécois are quite distinct from the non Acadian French populations of Southern Louisiane which resembled a neo-Haiti or Caribbean French mix). Have these populations migrate or be forced into these regions and you can then even ensure the new Cuban and Venezuelan populations are made somewhat French.
4. The obvious introduction of Irish immigrants, at this point it is hoped that NO is even bigger than otl and thus a viable port opposed to New York City. At this point, Irish immigrants will likely choose this point to land as it will be a noticeably Catholic nation. Irish immigrants arguably do better here to, as political office would be more attainable.
It must also be said that this country would extend the meanings of Latino to outside of Spanish speaking Americas. Louisiane already in otl state government has a law code that without the U.S legislative authority would be considered a Latino or Latin oriented state (when you read the law systems of Louisiane, it is almost entirely French and Spanish civil as opposed to the typical English common in other US states).