Here are a few thoughts to consider.
Charles Carroll believed, not unlike Hamilton, that the heinous, bloody acts of the French revolutionists demonstrated a denial of a higher good--civic or religious--and that if America followed that lead, it would, like France, succumb to despotism or it would dissolve into small fiefdoms unable to mange the government of a new, robust nation.
Americans had established a Constitution that enshrined certain fundamental protections. Hamilton, in particular, the leading voice of the Federalist Papers, believed that the threat of wanton violence by mobs unrestricted by constitutional guardrails, could overwhelm the delicate balance established by the new U.S. republic. The hooliganism of the French Revolution demonstrated by the decapitation of the King and the subsequent Reign of Terror confirmed Hamilton's worst fears because they trampled on the rights protected in the U.S. Constitution. If these actions in France were to take root in America, they could overwhelm the Constitutional safeguards so recently established.
Moreover, on a related point, the killing of the King and the subsequent Reign of Terror in France confirmed the risk that pulling down an established government without a well thought-out means of replacing that government, will lead to anarchy and tyranny, a result that was equally possible if the U.S. followed the French lead.
In addition, the French declared war on Spain and England in the early 1790s as a direct result of the revolution, and actively sought to have the U.S. enter the war as a French ally. Jefferson, Madison, and many Americans sympathized with France. Still, the new republic had no army or navy. If it were lured into war by French blandishments, it ran the serious risk of a defeat that would undo the successful work of the previous two decades and would invite Great Britain to resume hostilities at a time when the U.S. was unprepared to defend itself.