"The American and French revolutions have a lot more in common than many American conservatives are willing to admit. They were both products of the Enlightenment and, from a contemporary point-of-view, left-wing in their outlook. Of course, royalist and anti-Enlightenment conservatism has never really existed in America."
Absolutely, they were products of The Enlightenment, but I don't think "left-wing" is an accurate description of the political component of The Enlightenment. America got a lot of the Blame from the Nobility of Europe for "inspiring" the French Revolution - it was seen as a natural result of "Mob Rule": what happens when the ignorant masses are allowed to run their own lives in selfish ignorance.
I'd argue it had more to do with the English Civil War than the American Revolution.
Well, I believe the origins of the left-right division are from the time of the French Revolution when the proponents of the Ancien Régime sat on the right side of the French National Assembly while the revolutionaries of the Third Estate sat on the left.
America's version of Enlightenment was the Scottish version...a belief in commerce and "getting along" with others despite their imperfections, while French enlightenment wanted the "perfect" being (the intellectual) to rule.