As North America rifted from Europe and Africa, what was the continuous rift system called?

The rift system is known as pangea.

Explanation:

Millions of years ago the earth consisted of only one single continent and its name was pangea. It consisted of modern day Europe, Africa, North America and South America. Pangea began to break up after a rift happened between Africa, South America and North America.

This also resulted in the creation of a volcanic zone in a lot of places, leading to eruptions and spitting of ash in various places. Pangea is also known as the mid Atlantic ridge due to the continuous expansion of volcanic materials into the ocean basin.