Yes, the American Revolution dates were a factor in the fall of the Bourbon monarchy a decade later, because the people of France saw what the Americans accomplished, and they wanted the same thing. At the time, the Americans and the French were very friendly, so it is not surprising that the French followed the Americans into overthrowing their government.
French and American philosophers often cited each other during the American Revolution. Benjamin Franklin was an ambassador to France leading up to the colonies' break with George III. There is little doubt the courage of American colonists inspired the French Revolution. French admirals and generals helped the colonies defeat England simply because the French hated the English in the 1700s. After the Revolutionary War, the French monarchy was deposed when poor and starving citizens rose up against the king and his family.
The ideals which led to the American Revolution inspired the French Revolution. The social and political climate in France was very different from that of colonial America. Both wars were inspired by Enlightenment ideals, including the idea that the people should be free from the monarchy. France also was burdened by extreme debt and an incredibly poor populace as a result of the King increasing taxes to support wars.
No, the American Revolution did not affect what happened in France, even though it was only a decade later. The French simply got tired of being unfairly, and decided to do something about it, which is similar to what we did. They were not following us, just fixing their country.
Overall I believe the American Revolution may have helped get the French Revolution going because many people at the time would clearly have been able to remember hearing about the American Revolution. To say that the exact dates of this, however, are a direct factor in the fall of the Bourbon monarchy is probably drawing lines where there are none.