The full answer to this question is quite complicated. In short, the general social and power structure in America remained more or less the same during and after the revolution. The American Revolution was led mostly by those who were already highly educated and wealthy before the war started. After the revolution, those wealthy and highly educated people remained in power and designed the country.

The French had a tendency to execute, imprison or chase off most of the wealthy and educated individuals in the society. For instance, Jean-Sylvain Bailley had been Mayor of Paris and the leader of the National Constituents Assembly (the group that kicked off the French Revolution). He was a mathematician, philosopher and scientist. What happened to him? Head cut off. Or General Rochambeau who had extensive experience fighting in the American Revolution. He was imprisoned. Or Gilbert Romme who was a teacher and designed the French Republican Calendar. He was sentenced to death but committed suicide before they could execute him. Or Antoine-Francois Momoro who was a publisher and philosopher in the early stages of the revolution. Guillotined. The same holds true for many others in France during that time. Those that were knowledgeable but weren't killed or chased off generally knew to keep their mouths shut to avoid attracting too much attention.

The end result, you might say, was a bit of a brain drain. You ended up with mob rule.

Compare that with the US where most of the social institutions remained in place during and after the revolution. It was a revolution led by businessmen, lawyers, doctors, teachers, and military officers. Whereas the French Revolution, in large part, was led by starving peasants and demagogues who saw no problem cannibalizing their own.

A critical factor too is the fact that France was a major European power, so the French Revolution had the potential to spill over into other European countries. This led to other European nations, such as Austria, Prussia, Great Britain and others to attempt to crush it. Under threat, the Revolutionary government took extreme measures to protect itself internationally and domestically, explaining to some extent the reign of terror.

In contrast, Americans lived on the periphery, and were mostly left to their own devices.

Like Hanging_out said, the State was already very important in the French society. They had to invent a new way of thinking, a new model after centuries of monarchy. They were lost at that time on this question, I took nearly a century to have a stable political regime. While in America, people were on their own, the state weren't dealing with their lives as much as in France, before, and after that. Wouldn't surprise me that 90% of USA's population just didn't see anything change after that (if someone can confirm).