Why did the french establish settlements along the great lakes and the st. lawrence?

The French settled along the St. Lawrence River and the Great Lakes for a few reasons.

France arrived late to the New World after Spain, therefore Samuel de Champlain moved north and up the St. Lawrence River. Trying to find the Northwest Passage to Asia, Champlain moved west around the Great Lakes.

France sent few settlers to the Americas. Only male missionaries and fur traders stayed in the new land. Therefore, not many sustainable settlements were needed. Fur traders trapped where they needed to. Missionaries interacted and traded with the Native Americans such as the Huron.

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