Conversation so far:
how did the french attempt to secure their hold on the vast areas they claimed in north america
They founded widely separated communities, fortresses, and trading posts.
which areas in North America did the French  control
The French established forts and settlements that would become such cities as Quebec and Montreal in Canada.
what areas did the French control in the US
The French established forts and settlements that would become such cities as Detroit, Green Bay, St. Louis, Cape Girardeau, Mobile, Biloxi, Baton Rouge and New Orleans in the United States.

Question: what did their colonies produce
Self-contained rewrite: what did French colonies in North America produce