Let"s say Napoleon doesn"t get pancreatic cancer, or any other misfortunes befall him. Could Lord Cochrance, granted he gets him free. Help him set up a South American empire? What would the ramifications for this be.
If he lives longer and becomes ruler of Mexico, which was proposed by the Mexicans at one point I believe, then the USA is in for a nasty, nasty surprise when the Mexican American War happens. He died in OTL about fiftyish and assuming barring that or the theory the British poisoned him with arsenic (Cochrane finding out and putting a stop to that is a good POD) he has another twenty years in him plausibly, leaving him alive when that happened.
I do not think the US would be getting Texas, California etc. if that is the case.
Napoleonic Mexico if it happens would probably be a little before the US really got strong enough or paranoid to care, and he has experience improvising armies on the fly with some success. I think it was either Santa Anna or Iturbide who had the idea of making him emperor with some popular support for the idea.
It could really, really get nasty if he decides he wants the Lousiana Purchase back...
That's a massively big "if"!
Napoleon himself has no claim on Louisiana. He might, as the liberator and 1st Emperor of Mexico attempt to convince the Mexicans that they have a claim to it, however, projecting enough power to press that spurious claim would take the power of billions of butterflies.