Dark Comedy, Neo-noir, Crime Drama
Yeah, Fargo is a dark comedy—or at least plenty of people would call it that. In a way, though, it might be the movie's realism that makes it so darkly amusing. The criminals aren't super-villain masterminds or the kind of elite bad guys who populate James Bond films: they're just unscrupulous and incompetent weirdoes like the "dumb criminals" n those viral videos.
The good guys, on the other hand, like Marge and her husband, are seen doing things that plenty of real-life heroes would experience, but that you might not see in a more typical genre film. They eat Arby's, buy night crawlers, have morning sickness, and get a duck painting put on a three-cent stamp. You could view these as ironic touches, but they're strangely true to life. There's this implication that real life actually is a dark comedy.
As Joel Coen said in an interview:
We are often asked how we manage injecting comedy into the material. But it seems to us that comedy is part of life. Look at the recent example of the people who tried to blow up the World Trade Center [in 1993]. They rented a panel truck to use for the explosion and then, after committing the crime, went back to the rental agency to get back the money they left on deposit. The absurdity of this kind of behavior is terribly funny in itself.
Also, the movie can be categorized as a crime drama and "neo-noir." It uses some of the classic tropes of the film noir—digging into the seedy underworld of the lawless and corrupt—while at the same time reversing them.
Instead of having some Sam Spade/ Humphrey Bogart private eye as the main character, the Coens pick a pregnant small-town police chief. And they suck all the Hollywood cool right out of the criminal underworld; there's no luster to what these guys do. They're immoral and incompetent.