for being similar i will say they are the consequences of the "Lumières" (Enlightenment), with some ideals of constitution, liberty, self government, etc.
BUT, there are also VERY different :
-the American Revolution is more a revolt (against taxes) which became a war (it is a war of independence more than a revolution)
-The French Revolution is really different and it is more the failure of a system, what we called "Ancien Régime" (Former Rule), a system which can not work anymore since the 1770's (the nobles do not pay taxes for example when there is a MAJOR deficit). A system which blew up in 1789 when the king called the Etats Généraux (States General, see wikipedia) to enact new taxes, but the deputies decided to not do that and create an Assemblée Nationale (National Assembly) to write a constitution. the result is a real mess for at least 10 years (in fact 1 monarchy and at least 5 different republic during this time)
So yes they are a little bit similar (it is the Age of Enlightenment) but they are mainly different, because the American one is an uprising against something (the British) and the French is more the end of a system and the different experiences to find a new one.