Incorrect. The American Revolution was a direct outgrowth of Enlightenment thinking (Natural Law and Social Compact). The French Revolution was a product of Romanticsm (Liberté, Egalité, Fraternité: Liberty, Equality, and Brotherhood).
I disagree. The Enlightenment was the notion that rational thinking was sufficient to explain everything and this drove the French. The fact that they were more romantic should not be confused with the romantic movement, which (IIRC) proposed that some things were beyond reason and had to be understood by some other method.
The Americans recognized God as the source of unalienable rights. They also recognized the depravity of man, which caused them to build constraints into government because they knew fallen man could not be trusted. This was a specifically reformed notion. I have just finished "How Shall We Then Live" by Francis Shaeffer which has a pretty good chronicle of the changes in Western philosophical underpinnings. I'd recommend the read.