Both the Renaissance and the Enlightenment were based at least partly on the idea that reason could be used to understand and to improve the world. Instead of relying on past authorities and tradition as guides, people were supposed to think logically and rationally about the world. This applied to the world of science but also to society.
Both the American and the French Revolutions were inspired by these ideas. In both cases, people were asking why they should believe in things like monarchy and aristocracy. These were both based solely on tradition as there was no rational reason to think that God had anointed some people to have hereditary control over others. Because of Renaissance and Enlightenment ways of thinking, people in both countries came to believe that monarchy should be overthrown and more democratic and rational forms of government installed in its place.