While the French Revolution did not lead immediately to a true democracy in France, it did help to bring about more democracy in that country and in the world in general.
The French Revolution did this largely through its rhetoric. It is often the case that the rhetoric of a revolution can have more of an impact in the long term than the revolution itself has in the short term. In the short term, the revolution did get rid of the monarchy and the aristocracy, but it did not lead to a democracy.
Instead, the revolution provided a set of ideas. It was, of course, led by people espousing the ideas of “liberty, fraternity, and equality.” It also gave birth to the Declaration of the Rights of Man and Citizen. This document was something like a combination of the American Declaration of Independence and Bill of Rights in that it both explained the Enlightenment thinking behind the revolution and spelled out specific rights that all the people were supposed to have.
Even though France did not live up to these ideals right away, the ideals took hold both in France and elsewhere. They helped to introduce the idea that all people should be treated equally by the law and that they should have certain of their rights protected from government actions. This is a major aspect of democracy.