the French revolution, in general was extremely significant since in Europe, it could be seen that the state could be run without an absolute king.
the absolution of the monarchy, meant that a constitutional government could run the society.
Let's bear in mind that, the French revolution occurred in 1789, 8 years after the American Revolution, where the Americans set up a Republican government, mind you that the American Revolutionaries many of them were Enlightment-leaned, Jefferson being the most notorious.
so, from the Enlightment movement, one can see Liberty Leading the People, namely monarchy-free people can, as Rousseau would say, run the affairs themselves and be more effective and more freedom-enhancers than a monarchical system, or a church-based one.
so, the French Revolution occurred in the middle of the Enlightment movement and thus directly affected by it, just like the American, and as the motto of the Enlightment have it, "be courageous and use your mind to free yourself from the self-imposed chains", it showed that folks, in an organized fashion, can run the show more effectively than an absolute monarch.