Well, the short answer a short time would pass as Spain still continued to grow weaker would pass and another rebellion erupts.
If the POD accounts for some kind of policy changes that can remove the threat of rebellion in the form of some kind of compromised state where Mexico remains in the empire but somehow satisfied the economic and social divisions that existed (and still do) then perhaps the empire remains strong enough to keep other colonies in the New World. Most likely Cuba and other Central American states might remain in the circle, France likely doesn't directly interfere, American involvement in the region would be more limited or at least delayed. Perhaps French interest would involve more assistance to Spain rather than her own direct involvement such as canal or empire building allowing for a more successfully Latin state to immerge. Of course this probably would only bring about more of a separatist feeling to break away from Spain again.