Why did the french build a system of forts in north america?

There are many reasons as to why the French did that.

1. Native Americans were still the indigenous people of this area, some tribes being very dangerous. Having forts meant having protection, something the French valued highly in their new explorations.

2. There were no cities or civilized villages. Forts were the closest thing the French had to setting up structures to reside in while they explored the new world.