“The territory that became the “Louisiana Purchase” and just about doubled the size of the United States was French. Uh, no. “
Uh, yes.
Your confusing territory with inhabited. Back then, many countries claimed territory it never occupied.
Look up "couriers de bois". The French were all over that territory. And by virtue of possession of New Orleans and the Mississippi, they controlled easy access to it as well. The French actually explored far more widely than the Spanish in North America.