The French Revolution was a very complex event that covered a large span of time and included a number of different ideological variants. The Enlightenment was also very complex and multifaceted. So any answer to this questions is bound to be incomplete. However, the Revolution did reflect several important Enlightenment ideas, especially in its first, liberal phase.
First, the Revolution ended many of the privileges that had belonged to the French nobility. While this was not something many philosophes, many of whom were themselves from noble families, aristocratic privilege was a frequent subject of scorn from writers like Voltaire, who viewed it as corrupt and counterproductive.
Second, the Revolution placed the Catholic Church under state control, eliminating many of the traditional privileges it had always enjoyed. This was different from separation of church and state, but the revolution also established religious freedom in France.
Third, the Revolution established many civil liberties long advocated by philosophes, including freedom of the press, of religion, freedom against arbitrary taxation, and due process.
Even the more radical excesses of the Revolution were justified by pointing back to the writings of such philosophes as Jean-Jacques Rousseau, whose notion of the "popular will" was used to justify the violence employed by the Committee of Public Safety. On the other hand, the early phases of the French Revolution were in many ways based on the Enlightenment belief in basic human equality. And Napoleon certainly conceived of himself (with limited justification) as an enlightened emperor. So many of the intellectual foundations for the Revolution can be traced back to the ideas of the Enlightenment.
The enlightenment was actually the starting force of the revolution. Thinkers like John Locke advocated new ideas. Locke himself said that if the government or king is not doing their job to help the people, the people should be able to overthrow the people above them. As bad years of farming, mismanagement of the state's funds, and the bad gossip about the king and queen popped up everywhere, people started to follow the enlightenment ideas and revolting.