It would be called Nouvelle-Angoulême, you are correct. But like New York, it would be named after a person (in this case Francis I of France, Count of Angoulêm, and not the city of Angoulême.Veranazzo (sic) sailed into the harbor and called it New Angeloume (again, sic). That'd be a possible name, for starters.
But whatever else, French America got a huge boost. Now if it's its own colony, part of Acadia, or part of Louisiana that makes me wonder...