in fact, apparently there was no Louisiana at all, it was the new France. But the new France practically did not colonize these lands at all, they simply declared them the property of the king. There was only fur trade
Attempts at farmer colonization there were precisely from Britain, the Indians themselves fought with Britain, and achieved a ban on colonization. France apparently lost these lands already at the entrance of the Seven Years' War. But it weren't really French at all, they were just mouth opening.
Relations between the Indians and the British were regulated by the Indian Bill of Rights