They've spearheaded it. See especially Maximilien Robespierre and the Jacobins while still within his control (before the Thermidorian Reaction). He and other Enlightenment thinkers played a huge role. Voltaire was for instance the primary satirist of the French Enlightenment. It is important to also consider the connection with the American Revolution. How most of the thinkers were in support of it and even French troops were sent - where some thinkers served. The thinking there spilled over to France and was even further developed throughout it. Exploring that connection will definitely answer the question.

For more info see this https://www.quora.com/How-did-the-Enlightenment-influence-the-French-Revolution & http://www.history1700s.com/index.php/articles/12-french-revolution/125-the-influence-of-the-enlightenment-on-the-french-revolution.html