WOW!
Would you like to say that Napoleon would have been interested in what occurs out of Europe?
Frankly, it is all the history of the planet which would have changed.
It would have to take troops in Europe, therefore to consider its conquests differently. Probably an alliance between England and the USA.
It is even probable that that would have pushed it to pay more attention to the navy. The missed attenpt to conquer England does not put place.
And Villeneuve don't pushed to lose at Trafalgar (Nelson is not good for catch ennemies).
Two possibilities :
1° Napoleon give up. Really, it's go for a big change in the XX century.
2° Napoleon go to war and England allie with USA.
- Probably no russian invasion.
- Big efforts on the fleet.
- Lose, in a first time, of louisiana and Texas, but England pick a lot of territories for Canada. Today, USA lack of a lot of states in the in the North and North-west.
- If Napoleon can send a lot of troops in America (mexico ?), i don't see USA stand up. Only english troops can, and i don't know if England can send one of the few good generals they have (France don't have this problem).
Probably big changes in XX century (at this era, The USA are already seen like unreliable allies by french. Imagine with this attack. And imagine if USA is successfull...).
If Napoleon win, he's probably in better position in Europe. I see another History Divergeance : If, with this new territory, the possibilitie to build a new fleet here, and the invasion to Russia nullified or pushed latter, Napoleon can win or stalemate England, well, we can have French Stardestroyers at the XXX centurie
If not, maybe USA and England can retake the lost territories in America. If yes, USA take Louisiana (well, they have no right on, and traities say "France at her pre-war borders, i think) ? England jump on and pick a lot of territories in the actual USA ?
3° Napoleon go to war and England don't allie with USA (unlikely, for me).
- Maybe no russian invasion, or maybe latter.
- USA probably crushed. They don't have the sheer power, they don't have the good generals, they don't have the industrial base, they don't have the population, they don't have the experienced soldiers Napoleon have.
Probably big changes in the XXe century, too.