There is debate among historians about whether Enlightenment ideas were all that important in the outbreak of the French Revolution. Some historians argue that most of the important Enlightenment works were not all that widely read in France before the Revolution, and that those who read them were mostly nobility, the type of people who generally opposed Revolutionary reform. But there is no doubt that the revolutionaries expressed their ideas in terms of Enlightenment thought, even if there was not necessarily a direct line from the Enlightenment to the French Revolution.
Broadly speaking, the reforms that accompanied the establishment of the National Assembly in the first phase of the Revolution established a limited constitutional monarchy. Many of the philosophes, especially Montesquieu (who was dead by the time of the Revolution) had advocated this system for some time. Enlightened revolutionaries like the Marquis de Lafayette and the Baron de Condorcet envisioned a system not unlike that advocated by Montesquieu, which would be dominated by educated and sophisticated men like themselves instead of the corrupt court of the Bourbons. Many of the reforms enacted in the early phases of the Revolution, and even during the radical phase, reflect the influence of philosophes like Voltaire, who argued passionately for religious freedom.
Jean-Jacques Rousseau, a radical thinker who argued that government should reflect the general will of all the people, was influential in the more radical phase of the Revolution. Robespierre, director of the Committee of Public Safety, instituted his Reign of Terror and other reforms in an effort to enforce the kind of republican virtue that Rousseau thought essential to the maintenance of a free society. Rousseau, also dead by the outbreak of the Revolution, was openly venerated by the radical Jacobins who pushed the revolution in this radical direction.
Again, few historians argue that the French Revolution was a direct result of the Enlightenment, but most agree that the Enlightenment helped shape the course of the Revolution, and that it may have motivated many of the revolutionaries to seek the reforms they wanted.