Final answer:
The French settlers competed with the Dutch over the fur trade in North America, both establishing colonies that focused on this lucrative trade.
Step-by-step explanation:
The group of settlers that competed with the Dutch over fur trade were the French. Both the French and Dutch established colonies in the northeastern part of North America, with the central aspect of their colonies being the fur trade. The Dutch confined their operations to areas such as Manhattan Island, the Hudson River Valley, and what later became New Jersey, while French fur traders and missionaries explored regions such as the Great Lakes and the Mississippi River. This competition over the lucrative fur trade was a significant aspect of early colonial interactions and rivalries in North America.