The cod fishery began the early fur trade, the Mi'kmaq would trade with Europeans coming for Cod. The British would set up stations to dry fish on land but did not settle permanently. The French also did not settle but came for the fresh water. Overall the First Nations viewed it as a way to build trade, peace, friendship etc.
The Drive West
During the "Expansion Inland" the French dominated the Fur Trade, as well as New France being established, In between this there was also a war called the "French Haudenosaunee War ( Beaver War)" over beaver furs. The people would also travel on tributaries to transport the trading goods, and the Ouendat were Middlemen between the French and other French Nations. During this time there were also "Coureurs de bois" aka the runners of the woods.
Monopoly of the West
In 1670 during the "Rival Networks" Britain established the HBC. The HBC competed directly with the French. During this time the Hudson's Bay Company needed voyageurs and middlemen - between forts along the Hudson Bay. So the First Nations worked this role for both the French and the HBC.
Conclusion
During "The Drive West" the French were defeated by Britain in the "Battle of The Plains of Abraham". The British took over New France and the Fur trade operated under the British system of mercantilism. Then in 1779 independents merged together to form the North West Company. The competition between the HBC and NWC then drove the fur trade west.
In 1869 during the "Monopoly of the West" the British helped the HBC sell Rupert's Land to Canada, and the HBC also lost a court case against independent Meti Traders.