There is actually quite a bit of debate over this question. There has traditionally been a view, perhaps stemming from the French Revolutionaries themselves, that the FR was a triumph of enlightened values and liberalism over despotism and tyranny. This is also the view that you will most likely hear (or at least how it will come across) in most high school and intro university Western Civilization classes. The argument that the French Revolution was a direct result of the Enlightenment is however, not a terribly cogent one. The events that led to the formation of the National Assembly and the overthrow of the Monarchy are much more easily attributed to economic and political tensions that already existed in France (in some cases dating back to the sixteenth century) which were finally addressed by a popular attack on aristocratic privilege. The most secure link between the Enlightenment and the FR comes after the events of 1789 when the people who found themselves in power had to make sense of their new situation and find a way to order the new nation fell onto the works of the enlightenment with which they were familiar as a basis for the Republic. IN short, the strong causal tie between the Enlightenment and FR are more likely due to reading intent into history with the benefit of hindsight rather than a strong causal relationship.

Sources: Norman Hampson, The Enlightenment (Penguin Books, 1968)

Keith Baker, "On the Problem of the Ideological Origins of the French Revolution" and "French Political thought at the ascension of Lousi XVI" in Inventing the French Revolution (Cambridge, 1990)