I'm sorry but the question seems to be cut off before completing the question. It seems to be discussing the exploration and colonization of the Americas by European nations.
In terms of the European nations that colonized the Americas, the "Big Three" are typically considered to be Spain, Portugal, and England. France was also a significant European nation involved in colonization but is not always included in the "Big Three."
One reason that pushed France's continued exploration of North America was the abundant fur trade that made merchants rich. The fur trade was a lucrative business for the French in North America, especially in regions like Canada where beaver fur was highly valued in Europe for making hats. This economic opportunity was a major driver for France's exploration and colonization efforts in North America.
If you have any further questions or need clarification on any of these points, feel free to ask!
