There were already the beginnings of political parties in the US before the French Revolution, but the French Revolution sharpened the lines between them and helped make them truly distinct.
The French Revolution caused a war between France and England. The two parties in the US became more distinct as they took sides in this conflict. The Federalists sided with England because they were more conservative. The Antifederalists were more wedded to the idea of democracy and the will of the people so they sided with France. In this way, the French Revolution helped to define and emphasize the differences between the two nascent political parties.