Final answer:
The French government sent Samuel de Champlain to Quebec to establish a fur-trading outpost, form alliances with local Algonquian people, and compete with other European powers.
Step-by-step explanation:
The French government sent Samuel de Champlain to set up a colony in Quebec for a few reasons. Firstly, they saw Canada as a valuable location for the fur trade, which was a lucrative industry at the time. Champlain established Quebec as a fur-trading outpost and formed alliances with local native Algonquian people, who were essential for the success of the trade. Additionally, the French government wanted to establish a presence in North America to compete with other European powers, such as the British, who were also establishing colonies in the region.