The document summarizes the establishment and development of French colonial empires in Canada and Louisiana between the 16th and 18th centuries. It discusses the French fur trade with indigenous groups, the establishment of settlements, competition with other European powers, relations and alliances with native peoples, and the economic dependence of New France on the fur trade. Key events included the French allying with Algonquians and Hurons against the Iroquois, competition with the Dutch fur trade, growth of the upper country population, and maintaining alliances being critical to containing British colonial expansion.