The French Revolution caused a problem for the US because it forced the US to choose whether to favor France or Britain in a war between the two. After the French Revolution, Britain and France went to war. The US had trade relations with both sides and different groups of Americans supported each side. This caused difficulties for the US because it was very hard to know which side to support. The US had to make some decision because both sides were attacking its shipping as it tried to trade with the other side. These issues almost led the US to war with France and did help lead to the War of 1812.
Thus, the French Revolution caused a problem for the US because it led to this war with England that entangled the United States.
When the French Revolution began in 1789, the US was supportive. The French Revolution began with a lot of the same ideals, enlightened thought, and drive as the American Revolution. Unlike the American Revolution, the French Revolutionaries became increasingly more radical with political ideologies and liberalism as the revolution progressed. The US became more neutral to the French at this point. Despite radicalism ending with the end of the Reign of Terror, the US stayed cautiously neutral towards the French.
Once Napoleon took charge at the tail end of the French Revolution, he began fighting many wars with other European monarchies in order to spread French political influence and dominance throughout Europe. In order to finance these wars, because a growing rebellion in the highly profitable Haitian colony was preventing profits from reaching France, Napoleon sold off the large plot of French land in North America to the Americas. This was the Louisiana Purchase.
Let's fast forward to the War of 1812. Napoleon and the British were fighting each other, and each were trading with the United States. In order to negatively impact the other's economy, both Britain and France attempted to blockade trade between its enemy and the United States, thrusting the United States into the middle of war. This culminated with the War of 1812.
To recap: the French Revolution was supported initially by the Americans, but as the French became increasingly liberal and revolutionary, the Americans decided to remain neutral. Because the Americans had trading relationships with both France and Britain, when Napoleon went to war against Britain, the Americans became a focal point for the conflict. This led to increased tensions between the British, French, and Americans, and erupted in a territorial conflict in America, known as the War of 1812.