I wonder how the French being spoken would change? Would it adopt more English and Spanish loanwords? Native ones?
Well there are already oddities in French spoken in southern Louisiane. Most notably:
Chaoui-raton laveur-raccoon
The infamous, this causes the most difficulty in mutual communication: ayou-où-where
Moyeu-centre du village-middle village (the word is derived from middle)
Ouaouaron-grenouille-frog
Tchac-Oiseau-bird
Plaquemine-Kaki-Persimmom
Bayou-taken from Louisiane french-même
Barbue-poisson chat-catfish
The oddity of; paistre-dollar-dollar
Soulier-chaussure-shoe
Tcheu-queue-tail
Drette là/asteur là/asteur-maintenant-now
Guetter-regarde-look at/watch
Étoufée-étoufée (la même)-asphyxiation (étoufée in the NO context is a good dish whereas it is asphyxiation in standard French, how's that for an oddity?)
And many more oddities, that can be found by visiting some of these communities in southern Louisiane.
The above vocabularies are only those shared by both Plantation French of Nouvelle Orléans and other areas in the NO metro and the other dialects such as the wider Cajun dialects or the Plantation French in Aveyolles.
In terms of Muskrat and Missouri french, these are more difficult to track. I can try to do some research.
In this scenario we will see the same development of Plantation French as otl, an r that rolls more similar to Spanish as opposed to the more guttural standard French, this can be seen in the pronunciation differences of the word rue (road). English words will also become common, or so called anglicismes, with technical terms being likely English oriented unless active moves are made to remain purely francophone in terms. So you could see, the otl use of say traîn for train.
African influences would still be around, specifically in the NO metro areas. This would especially be common as it is otl in the heavy consumption of rice and other African influenced cuisine in the area; whilst Acadiana seems more like a rural and adapted french peasant cuisine (all of which is otl). In this scenario food from Louisiane will likely become even more famous than otl and would possibly be consumed in other francophone countries as a sort of exoctic yet also kind of similar food.
Thus we have a Louisiane split along certain differences:
La Nouvelle Orléans, Métairie, Chalmette, etc... would essentially become as it did otl but more firmly francophone. That is, a neo Sainte-Domingue and one of cultural mixing, specifically of African, Spaniard and French. It also could mix a New York City to greater New York relationship with the country side around it. This is also where the urban elite will be and likely the first capital of the state.
Vermillion (Lafayette), Pont Breaux, Lac Charles, Nouvelle-Iberie, etc... would be and is the base of Acadiana, the power base of a large rural and fishing population. These areas would also be much more religiously conservative as they were otl compared to the liberal NO.
Aveyolles, Châtaignier, Natchitoches, Alexandre, etc... or the central part, would develop to be a mixing of cultures as well as the center of the Plantation economy of this state. Likely the rural aristocrats will inhabit this area as they did otl until after the civil war.
Shreveporte, Ouachita, Lac Caddo, Blanchard, etc... this is where things begin to change. This area harbors and more so then, a tiny Créole population and a medium sized Cajun population in Shreveporte/Lac Caddo/Blanchard, but these areas where quickly inhabited by Anglo settlers and was the first area to become monolingual in another language other than French in around the 1840s. The development of these areas is up for debate. However, it is a rich area and Shreveporte will be extremely important on the Rivière Rouge and Lac de la Croix. So this could be the earliest haven for migrants not staying in NO. Further if seethed before 1840 in large numbers, it will remain heavily francophone.
The Ozark mountain region could do any number of things. Most likely of which is that any migrant population mixes even more heavily with native populations than otl. The only city in the area would be Arcansea poste which is only an Indian trading village. This was by far the weakest of the francophone cultural zones. Also migrants will likely pass it by and go to Missouri.
Francophone Missouri is most known for its fur trade and merchant populations huddled in its cities. Primarily, Sainte Louis which experienced rapid growth during Spanish occupation as a consolidation of the merchant families in Missouri left from Nouvelle-France. What this develops into is at discretion of the writer. Also these colonies and peoples were the successors of coueurs de bois and other adventurers.
Further west, I am not sure of.
Détroit is under American control, but it was the other major area of Francophne inhabitants known for its Muskrat French which helped create the famous fur trade in America as a gateway city.
An interesting scenario in my opinion from a cultural view.
