The French Revolution was in many ways an outgrowth of the American Revolution, based on many of the same democratic ideals. France had also been a valuable ally in the American Revolution, without which victory against Britain might have been impossible. For these reasons, Americans were broadly supportive of the French Revolution initially.
However, as the revolution dragged on, the instability in France got worse, and some of the revolutionaries in France were too radical even for the American revolutionaries.
Attitudes toward France became linked to existing political divisions in the US.
Thomas Jefferson's Democratic-Republican Party was in favor of the French Revolution, based on its democratic ideals.
Alexander Hamilton's Federalist Party was largely opposed to the French Revolution, due to the disorder it had created. Hamilton was also interested in restoring ties to Britain as a valuable trading partner.
In the 1790s, the French became increasingly radical and several monarchic countries in Europe (including Britain) rose up against them.
American sentiment turned against France when in 1794, during the infamous Terror, the French arrested and detained Thomas Paine, who was an American citizen and an important activist. The Federalists took control of the US government and severed ties to France, resulting in a series of diplomatic incidents culminating in a cold war with France called the Quasi-War.
A few years after that, Napoleon seized power over France, and hardly anyone in the US was willing to support France anymore.