The Americans talked a lot about checks and balances; the French talked a lot about liberty and brotherhood.

Different political situations. Even before the revolution, the American colonies had pretty much functional governments at what we'd now call the state level; the political problem that needed to be solved after the revolution related mainly to how those colonies could be integrated into a national government. Most of the famous documentation relating to the process (and most of our present-day impression of an emphasis on checks and balances) comes from the second attempt at doing so; the first lasted only a few years.

The French Revolution, on the other hand, was attempting to build a new system from the ground up, and was concerned with ensuring that that system would emphasize individual rights rather than the ancien régime's hierarchy -- a concern that reflects itself in the rhetoric of the time.