What outcomes did the battle of Alesia have on modern day France?

With victory at Alesia, Caesar conquered Gaul. Under the Romans, Gaul became latinised. This is the origin of France being a Latina country and the French speaking a romance language (a language derived from Latin. The only remnants of Celtic culture is in Brittany, and that comes from Celts who migrated form Cornwall, not from descendants of the Gauls.