The French Revolution was the event that kick-started the spread of democratic ideas and regimes throughout the Old World. It brought about the downfall of the medieval regimes, the abolition of serfdom and slavery, etc.
The American Revolution was more of a symbolic event at the time. On the other hand the fall of the French monarchy was a colossal event at the time: the new French Republic was continuously attacked by all its neighbors to prevent the dangerous ideas from spreading.