Republicanism in France and the United States derived from differing contexts and principles. American colonists recognized in the ancient world a slave society they recognized as somewhat similar to their own (See The Wolf By its Ears - a history of Thomas Jefferson and U.S. slavery by John Chester Miller).

For French republicans, who came to dominate the political landscape by the late 19th century, slavery was restricted to territorial possessions outside Europe (see Bret Rushforth's Bonds of Alliance). When the Revolution came, Jacobins in France emancipated Blacks in the empire's New World colonies in a beautiful moment that to my mind redeems republicanism as an acceptable political ideology (see CLR James' The Black Jacobins).

Unfortunately, and this is where you must be a little careful with these comparative notions of history, French thinking was not anti-racist. Napoleon rescinded the revolutionary order to free the slaves. The Haitians rebelled. Emancipation for France's other colonies did not follow until 1848's Second Republic. And then you should see Franz Fanon, Michel Foucault, and Edward Said for sustained critiques of the constitutive role racial thought played in French (and other Western nations') psychological, intellectual, and aesthetic developments since the origins of imperialism. France is not less racist than other places. But there has historically been less cause for that society to target Blacks from the Americas. Instead, they marginalized and stigmatized Black Africans, Arabs, Vietnamese, etc.

Just an obvious point: France does not have an African-American community... (Well, there are the Caribbean islands, but that's it). People with (recent) African ancestry are are just known as “black” (in French: noir, renoi, black).

edit: as precised by /u/kapparunner, there are some African-Americans in Paris, but I still leave a warning for the readers that “African-American” is not a synonym for “black”...

There were several fantastic answers on this subreddit about post-Civil War racial relations in the US, but they were not wikied (they should have been) and the “search” button is a bit nasty with me right now (telling me that /u/yodatsracist barely ever wrote in /r/Ask/Historians, wtf?), but the correct answer would not be that the French were less racist than the Americans, but that the Americans, due to a complicated history involving slavery, were more racist than the Europeans.

Here is an example, the discussion of post-Civil War segregation in Detroit, with lots of links to other discussions on the topic.