An oft-repeated claim comparing the American and French Revolutions goes something along the lines of "the French Revolution was based on the Enlightenment, while America's was based on Christianity," or another variation is, "the American Revolution holds that rights come from God, while the French believed rights come from the people or government only." Admittedly, I know more about the American Revolution than the French (so perhaps Kuznicki will chime in), but my research tells me these claims are wrong, that both the American and French Revolutions were based on the same Enlightenment principles, which were relatively novel for the time ("the new science of man").
As Francis Fukuyama put it in a Booknotes interview about his classic, The End of History and the Last Man:
Now, by the French Revolution, we don't mean just the limited historical event; what we mean is the emergence of what we understand as modern liberal democracy because in the French Revolution, ultimately what it was about was a revolution in favor of the principles of liberty and equality. Now you could substitute the American Revolution for that because, I think in that kind of ideological sense, those two revolutions were equivalent. I mean, they were both revolutions to create what I earlier defined as a liberal democracy as a political system based on popular sovereignty with guarantees of individual rights.
This isn't to say there weren't profound differences between the two revolutions; clearly there were. But at base, they appealed to same Enlightenment principles. This shouldn't be surprising; Jefferson, the author of our Declaration of Independence also, while in France, assisted in writing the French's Declaration of the Rights of Man. The Declaration of Independence was also heralded in France and helped spark their revolution. It's no wonder that the two documents are quite similar in what they say.
The way both nations approached these revolutionary ideas was quite different. To repeat, these Enlightenment principles were revolutionary, that is they were anti-traditional. In both societies many traditional practices, customs, laws, and institutions were antithetical to these principles, slavery being the most obvious, but also monarchy, feudalism, established Churches, religious tests, and many others. The French attempted to "sweep away" all those practices and institutions, inconsistent with these Enlightenment principles, and remake society, going so far as to start the calendar over from "year one." Their society went into convulsions.
America on the other hand, allowed as a compromise many of the institutions which were inconsistent with our ideals of liberty and equality. But in doing so there existed a great tension between the revolutionary anti-traditional principles upon which we were founded and the illiberal traditional practices like slavery, state-established Churches and religious tests, and other "compromises" with liberty and equality. But because there was such a tension, history in the US marched in the direction liberty and equality and most if not all of these illiberal institutions were eventually ended because of our foundational principles. Obviously the American approach to liberty and equality turned out to be superior to the French for no other reason than their society went into convulsions and ours didn't (but then again, they had an established Church to disestablish, and a monarchy to unseat).
Also, contra the claim "we followed Christianity, the French, the Enlightenment, or America is based on God given natural rights, the French, government granted positive rights," in reality, the theoretical approach to God and rights was nearly the same in both the American and French Revolutions.
Again, given that Jefferson was one of the main "idea-men" behind both Revolutions, this shouldn't surprise. Both made supplications to an always undefined, generic God, never explicitly referencing Him as the God of Scripture (even though, in many minds He probably was). And both invoked God as the ultimate guarantor of rights.
For instance, in all three Declarations of the Rights of Man (one, two and three), God is invoked. First, "Therefore the National Assembly recognizes and proclaims, in the presence and under the auspices of the Supreme Being, the following rights of man and of the citizen." Then in the following two Declarations, "proclaim(s) in the presence of the Supreme Being the following declaration of the rights of man and citizen."
True, these supplication are nominal and vague, but American supplications to God in our Founding documents and pronouncements (given by our key framers) are similarly nominal and vague! Indeed, the American Constitution is entirely Godless save for the customary way of stating the date, "In the Year of our Lord" and in invoking the "blessings" of liberty (and the French, likewise refer to natural rights as "sacred").