They would have given [New Orleans] back to the US since the war was already over and the peace treaty resetting things to antebellum was already signed.
Except England didn't recognize the Louisiana Purchase. If England had taken New Orleans, they would be in a strong position to say that the territory is still Spanish and the legality of the treaty would probably go to the "Might makes Right" principle. And of course, since Spain is so busy rebuilding, England would happily agree to purchase the territory (or at least put some forts in there to protect it from the evil, expansionist Americans).