You'll note I have given up on the term 'explorers' in my title, for as I've done more reading I have come to the impression that most 'explorers' did only a little more than follow their native guides. Native peoples they met directed them, drew maps for them, guided them, and often even provided the paddling crew. They taught them to make and repair birch-bark canoes, paddles and snowshoes; they taught them how to survive in the wilderness.
We tend to glorify fur traders too, forgetting that it was the native peoples who actually did all the trapping and provided all the furs. The fur traders only gathered these in, trading metal trinkets for them before they got sold in Europe for enormous profits.
The third dimension to be considered in the first two centuries of contact is the role of natives as warriors. First the French and then the British negotiated with Indigenous tribes as their allies, and fought together in times of war. One of the very first examples was Champlain accompanying a group of natives from what is now the Montreal area south into Iroquois country on the American side of the border. In a very short battle Champlain fired his gun killing two Chiefs, and the Iroquois (Haudenosaunee) fled. Natives played a key role as warriors and allies right up until after the War of 1812.
Of course the first 'explorers' planted their flag and claimed the land in the name of their king, secure in the 'Doctrine of Discovery' (supported even by the Pope of the times) which claimed that European countries could claim whichever parts of the 'undeveloped' world they found, completely ignoring the fact that their were people already living there!
Never-the-less, particularly in support of trade, the French and later British negotiated 'peace and friendship' treaties with the Indigenous tribes, which set the background for working together. We tend to forget that native groups had negotiated their own peace and friendship treaties between tribes for centuries, and were thus able to trade back and forth across very long distances. In some parts of Canada such as between coastal and interior British Columbia, inter-tribal trade was very important.
It came naturally then for native groups to meet the French and British on the same terms, and mostly peaceful co-existence followed. However a conflict in understanding what a treaty actually meant between natives and the Crown became a major source of tension by the mid-1800s, 200 years after first contact. Natives saw treaties as meaning they would share the land and resources. The white government saw treaties as real estate deals which meant the government had purchased the land.
Cartier in 1534 explored the Gulf of St. Lawrence, and in 1535 returned to visit both Stadacona and Hochelaga, native villages where Quebec City and Montreal now stand. Champlain followed from 1603 to 1615, making more than one trip and gaining the friendship of the Wendat (known to the French as the Hurons). This enabled the formation of the Jesuit Mission at Ste. Marie among the Hurons a few years later.
Exploration continued through the Great Lakes and further west with example after example of natives leading the way, and often being responsible for the very survival of the white 'explorers' who followed them. Samuel Hearne provides a great example. He made three trips trying to access the Arctic coast, the first two aborted due to starvation. For the third trip he finally abandoned taking his white support crew entirely and travelled by himself with a native band led by Matonabbee. This trip was successful.
The infamous Franklin expedition to the Arctic is the best (or does this mean worst) example of ignoring native advice and assistance. It is said that Franklin and his men could have all survived had they sought native assistance and followed their advice - but he was secure in the superior knowledge of the Royal Navy! The pattern of natives advising these followers continued all the way to the west coast when Simon Fraser reached the Pacific at Vancouver in 1808.
The Fur Trade