Texas and Florida can be done by a richer Spanish Empire with less monopolistic trading and settlement practices (i.e, no limiting initial settlement to just Castilians until the 1700s; more ports to be able to do legal trading in) alongside keeping Portugal in the Iberian Union for the extra settler base. Texas in particular has good cash crop and ranching land that can attract a steady stream of settlers (and wine growing territory as well- an essential for every Spaniard
). Economies would be limited and too focused on extraction at first but hey, that's almost everywhere in the empire. Of course, Texas would require more connections to Mexico proper and the establishment of a militia system early on to protect from Native raids, but if that's done and the region is secure I'd see no reason why it wouldn't become heavily populated given a few generations ala Chile. And like Chile, it'd probably be split off into its own Capitan Generalcy early on to save more money from Veracruz's tax collectors.
Now the settlers don't have to be Castilians or hell other Romance speakers; later cases of immigrants from Ireland or Germany have assimilated just fine into the New World Colonial systems and very quickly losing their native languages. So I'd say just opening up immigration to willing Catholics would do the job.
As always with my go to solution to the Spanish Empire's problems, the earlier an internal free trade can be developed the more populated and powerful it'll be. In doing so here, you can see settlers eventually decide to expand from their bases of Texas and Florida.
Don't really know about New Orleans and the rest of the Deep South. Maybe France plants colonies there based of cotton, indigo, sugar and other cash crops? It'd be an easy way of making money- certainly would attract more people than Quebec at first. And from sugar comes a whole bunch of supporting industries that eventually create booming towns, with the demand for labor causing more and more settlement.