The short is no, but for a variety of reasons.

The comparison fails for a few reasons, but first and most important is the comparison of war. Early Modern Warfare was relatively light on involvement of the people and the nation beyond cost. Armies were much smaller than in WW1, with cost held on the state and the responsibility of equipment focused on state purchases. As such, there is VERY to little no burden on the populace in respect to warfare. As such, the people couldn't get exhausted from the American Revolutionary War.

Further, to compound it is the real contribution of the French, material. While the French did some troops, such as the expeditionary division under Rochambeau, the larger importance of the French was in money and material, with as much as ninety percent of the gunpowder used by the Americans being made or procured by the French.

However, there is... some importance of the American Revolution on the French people. As a result of the American Revolution and the money invested in them, the French Crown faced bankruptcy. While the people were tired, hungry, and angry with the nobility, there was NOTHING ready for the people to rise up against them. It took the assembly of the Estates General to bring the matter to anything to something that is beyond the Royal hands where a mere matter of parliamentary procedure derailed everything. (the parliamentary procedure was the matter of counting votes, the 2nd Estate (the nobility) wanted to count by voting block (essentially by Estate, where the 1st would side with the 2nd) while the 3rd Estate wanted to vote by head, thus ensuring a popular vote).

So, no, the French lack war exhaustion comes more from the mechanics of warfare at the time than anything else, thus preventing the Revolution from being similar to the Russian revolution.