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.
The French Revolution of 1789-1799 followed on the American Revolution and was inspired by similar ideals, albeit in different circumstances. A key element in the Revolution was revulsion against the inequalities of French society, not just as they were common in people's lives but also in so far as they were enshrined in the legal and political system, in which certain rights and positions were only open to those born of noble families. This was a period in which vast wealth and power accrued to the nobility and clergy and commoners had few legal or political rights.
The initial aim of the Revolution was to create a Republic in which all people were equal before the law, had equal rights, and had freedom of speech and religion. It envisaged a purely secular government rather than the previous system in which the Roman Catholic Church and the state were intertwined. Although the French Revolution eventually, after an extended period of turmoil, degenerated into the Terror and then the dictatorship of Napoleon, its initial ideals were democratic, including secularism, the rights of women, the right to freedoms of speech, religion, and assembly, abolition of hereditary privileges, and redistribution of property. These ideals eventually became enshrined in the democratic government of France in the second half of the nineteenth century and are central to French society today.