As far as I'm aware, the French revolution wasn't influenced by the American revolution to some profound depth. If there was any influence, perchance it would come in the form of the belief that things can change and that the people don't have to be passive subjects.

First and foremost, I'd argue that it's imperative to remember that before the French revolution, the feudal character of serfdom itself had changed somewhat in comparison to other countries at the time. "The peasant was, it is true, no longer bound to a particular manor; he could buy or sell his land at will, could marry without consulting the lord, and could go and come as he pleased. Many bought their land outright, while others disposed of their holdings and settled in town."^[1] The difference, of course, is that the older composition of the serfs as a class meant that they were bound directly to the land and had to ask of their lord many permissions- often of things which were intrusive into their deeply personal lives, such as marriage- before they could act. Now, it was different. But, "the lord might still require all those on his manor to grind their wheat at his mill, bake their bread in his oven, and press their grapes in his wine press."^[2] This was, of course, all at a cost. Also, "[many] of the old arrangements still forced the peasant occupying a particular plot of land to turn over to the lord a certain portion of his crops, and, if he sold his land, to pay the lord a part of the money he received for it."^[3] In this of light evidence, it should be noted that there were some reforms that separated the characteristics of the French peasantry from that of the traditional serfs as a class.

In terms of revolution, its main expression began in the meeting of the National Assembly, convened in 1789 under the directive of King Louis XVI as a method of allowing the people to express their grievances with the Ancien Régime. Many of the injustices felt by the French people- extrajudicial arrest and execution, arbitrary law-making, crushing tax burdens, church oppression, etc.- were expressed within this through the representatives of the Third Estate.

One method out of this was Louis trying to play the 'benevolent despot,' so to speak; and so Calonne stated that to make things better, they must "reform everything vicious in the state," which culminated in a reduction of the taille (one of the heaviest taxes known), reformation of the salt tax, scrapping of interior customs lines, and to correct the abuses of the guilds.^[4] In spite of vain attempts, indecisiveness drove the representatives of the Third Estate to eventually swear the 'Tennis Court Oath,' or the declaration to fight- to the death- for a constitutional Monarchy.

This then goes on to present many problems in contrast to the American revolution. While the Americans scrapped the monarchy altogether, the French initially did not, and rather sought to reform it and constrain the King to constitutional measures. It took the French 4 more years- and, in that time, many blunders on behalf of Louis, one of the most infamous being the failed 'flight to Varennes'- to finally declare the monarchy obsolete and show it through the guillotine. In those 4 years, however, there were constant attempts to form a constitutional monarchy, with some of the most turbulent periods sometimes ending in the call of 'long live Louis!' Even then, decades after the Jacobins were torn from power, Napoleon eventually declared himself Emperor of a French Empire, and even reinstated slavery in the colonies! The American revolution, in contrast, was much a revolution from a colony, and not the heartland of a despotic feudal order- arguably, their fight was much more direct and short-sighted in terms of goals, i.e., remove the monarchy and form the United States. In contrast, the French revolution aimed at an entire systematic change of the societal and economic modes, with future state socialists taking inspiration of the likes of the 'Conspiracy of equals' and Jacobins.

EDIT: Some spelling errors corrected.

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Sources:

1. James Harvey Robinson, Medieval and Modern Times, 1926;

2. Ibid;

3. Ibid;

4. Ibid.

I studied the American revolution's impact on European revolutionary movements a while back for an essay. My knowledge of it is pretty basic and so hopefully someone else could provide some further information on the topic. The American revolution as a whole was far more influenced by the enlightenment movement in Europe and specifically France. The revolution in the colonies was putting into practice what European intellectuals had merely discussed in their Parisian cafes. Public opinion in France for the revolution was rooted in a 'jingoistic anglophobia'(1) developed during the recent wars between Britain and France and individuals such as John Paul Jones, Joel Barlow and Thomas Paine helped bolster pro-american sentiment in Europe through their involvement in European intellectual debates etc. Its difficult to say whether events in France would have unfolded any differently at all and it's influence is probably only seen in some constitutional forms and reforms (2). However, the most tangible example of the American impact is seen in the peasant soldiers who served in Rochambeau's army. They witnessed the prosperous life of small farmers who didn't have the burdens of seigneurial exactions and high taxes that plagued French farmers. The regions from which the soldiers were recruited were also the first regions which experienced the worst rioting in 1789 against the ailing feudal system (3).
(1).- Blackwell encyclopaedia of the American revolution, Greene and Poole, pg. 519. (2). blackwell- pg. 523. (3). blackwell - pg. 523. tl;dr- It gave European/ French intellectuals a canvas on which their own ideas about egality and liberty were painted. It tangibly demonstrated that their own revolution might work. However, they already knew that and things probably wouldn't have turned out any differently anyway apart from perhaps to remove some doubts from their mind and some potentially minor changes to their own constitution.