CSA wins, then collapses... well, the USA comes back on them. End of story.
No way Britain or France is going to prop up a failed state. No way is the USA going to allow France to try to barge in on any bit of the rightful USA lands, such as Louisiana, regardless of historical claim. Mexico going at Texas will end the same, with the USA pouncing.
Tennessee would be the first to rejoin the Union, and that location would put a single state between the Union and the Gulf Coast, from Mississippi all around. None of the southern states have any sort of economic or industrial backing on their own to hold off the Union. They didn't as a Confederacy, so solo is a quick story.
No, no matter how you play things out, ANY USA worth its salt post-Civil War is going to face down ANY foreign aggressors on the simple principle of 'once an American, always an American' if only for the simple fact none are going to let others in their backyard.
Britain isn't stupid enough to try to support a failed state, as I said. France follows Britain's lead. Mexico has its own problems. Spain's empire is already in shambles, so same deal.
Basically, no outside player is capable or willing to contest/conquer the failed CSA, and the USA isn't going to sit idle while someone wipes their asses with the Monroe Doctrine. This means it's only a matter of time before the former CSA is slowly reincorporated to the USA. Either by hook, crook, or simple despair the CSA states will rejoin the Union eventually.