Why did the economy of the french colonies in america 's depend on a good relationship with native americans

Because of the fur trade.

The fur trade was main form of economy for the French colonies and the French got their fur from you guessed it, Native Americans. French colonists are an exception when it comes to dealing with Native Americans as they had good relationship with them and did not thought of them as inferior. They traded European goods for furs and the Native Americans even helped them by showing them goods hunting spots. So their relationship was one of cooperation.