Final answer:
The coureurs de bois served as the middlemen in the fur trade for both the French and British, forging crucial ties with Native tribes and aiding the economic success of the respective colonies.
Step-by-step explanation:
The individuals who acted as middlemen for both the French and the British in the fur trade were the coureurs de bois. These independent traders were Frenchmen who operated outside of the official frameworks set by the government or companies like the Dutch West India Company (DWIC). The name coureurs de bois translates to 'runners of the woods,' which is fitting given their extensive work with Native tribes to trap and trade fur, primarily beaver pelts, throughout New France. The coureurs de bois were pivotal in the establishment of trade networks, and often assimilated into native customs, fostering trade relationships which were crucial for the economic success of the French colonies, as well as the British through proxy alliances with local tribes.