I can't speak for the period extending to the War of 1812, but in the early 1790s opinion was very divided over Revolutionary France. It was one of the biggest political issues at the time in the US, and was one of the initial events that solidified the opposing parties of Federalists and Anti-Federalists. There were of course exceptions on both sides, but in general the Federalists were opposed to an alliance with France or even staying on good terms with them. Some hardcore Federalists such as Hamilton wanted to publicly disavow the French Republic and even form an alliance with Great Britain. Washington agreed with many of Hamilton's arguments and relations with the British were significantly improved in the mid-to-late 1790s, with many outstanding issues (e.g. British forts on US soil, escaped slaves) from the War of Independence being settled fairly, and trading privileges between the two nations agreed upon. Washington however drew the line at forming an alliance with Great Britain, as he was a firm believer in staying completely neutral from European affairs.

The Anti-Federalists, led by Jefferson, strongly opposed these pro-British moves and pushes incessantly for a more hostile attitude towards Britain and even closer relations with France, based less on the economic and mercantile reasons of the Federalists and more on ideological and sentimental reasons; Jefferson and the Anti-Federalists thought - with fairly understandable reason - that it was abhorrent that the US was becoming friendly with the country they'd just spent seven years at war with and was ruled by a monarch, while spurning the country that had aided them in their war of independence and was now a republic fighting their own war for their liberties (as the Anti-Federalists presented it). The Federalists - including Washington - countered that the treaties they had with France were signed with the Bourbon dynasty and its government, which had been violently overthrown, making the past treaties and relationships null-and-void.

Jefferson spent the early-to-mid 1790s as the American ambassador to France, and he saw the Revolution unfold in person, since he lived in the heart of Paris. At first Jefferson was ecstatic that France was following the US in the fight for liberty and republicanism, and his reports back to the US government were glowing. When things became more chaotic and violent, and when the Reign of Terror began, Jefferson still had a positive outlook at things, and insisted that the brutal actions of the French government was necessary to protect the revolution - hence his famous remark: "The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants". The Federalists back in the US, however, did not take such an optimistic view of things, and saw the French Revolution as being illegitimate because of how bloody it had become.

Jefferson and the Anti-Federalists' opinions on the French Revolution only changed when Napoleon came to power. When Napoleon overthrew the "republican" government in 1799 and became essentially a military dictator, it angered and alienated many of France's supporters in the US. Jefferson was quick to distance himself from the new regime in France, and after that point said very little about France in public. Federalists like Hamilton and Adams naturally took a "told-you-so" attitude, as both of these men had previously compared Napoleon to Julius Caesar, intended unfavourably. Both of them warned against the dangers of a military strongman coming to power in times of chaos caused by revolution, and said it was what they had tried so hard avoid in the US. Napoleon's coup further strengthened the pro-British and anti-French rhetoric of the Federalists and suppressed much of the opposition to the Federalist-run government's pro-British policies. Being pro-French and pro-Napoleon was, to use a modern phrase, very politically incorrect in late 1790s and early 1800s America.

During the presidency of John Adams (1797-1801), Hamilton even went so far as to suggest declaring war on France, with the newly formed (and very small and weak) US army. Adams wisely shut this idea down in its infancy, and he strove hard to find a peaceful solution to the XYZ Affair, or the "Quasi-War", between the US and France. Adams despised Napoleon and what the French Revolution had become, but he was smart enough to realise that the US needed peace and not war at the current time.

Sources:

John Adams by David McCullough

Hamilton by Ron Chernow