What enterprise did both dutch and french colonists pursue?

The enterprise that both Dutch and French colonists pursued, was fur-trading, more specifically beaver pelts.

On one hand, when Dutch realized the wealth of furs (specially beaver pelts), they found a reason to claim for the Netherlands, the north part of the Americas. The Dutch named their colony New Netherlands, and used it as a fur trading outpost in order to expand and give power to the Dutch West India Company.

On the other hand, French colonist while exploring the New World fostered friendly relationships with the native locals in order to encourage successful trade. For French colonists at that time, their main interest was establishing commercially viable colonial outpost. And that's why, they relied on native hunters to harvest furs (specially beaver pelts), and to exchange them for some of their French goods.

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