France founded a colony in Quebec in order to —

A.
establish a fur trade.

B.
establish a diamond trade.

C.
establish gold mining operations.

D.
establish large agricultural operations.

The correct answer is A. France founded a colony in Quebec in order to establish a fur trade.

To arrive at this answer, we can use a process of elimination. Let's review the options:

B. Establish a diamond trade: Diamonds are not typically found or associated with Quebec, so this option can be eliminated.

C. Establish gold mining operations: While there is some gold mining activity in Quebec, it was not the primary reason for France founding the colony. So, we can eliminate this option as well.

D. Establish large agricultural operations: Quebec's climate and geography are not particularly conducive to large-scale agricultural operations, making this option unlikely.

This leaves us with option A, establishing a fur trade. During the 17th and 18th centuries, fur trading was a significant economic enterprise in North America, and Quebec, with its vast forests and abundant fur-bearing animals like beavers, provided an ideal location for France to establish a colonial presence and engage in the fur trade.

Therefore, the answer is A: establish a fur trade.