Fargo is supposedly based on a true story. It isn't. The Coen Brothers (eventually) tried to weasel their way out of this by saying that everything in the movie was meant to be interpreted as fiction, including the blurb at the beginning that claimed it was based on a true story. Another lie they fed the media was that there was a news report in 1987 about a businessman who planned on having his wife fake-kidnapped for ransom money, but the police caught him before he could make his plan come to fruition, and the Coens asked themselves "what if he had succeeded?" On the special features on the 'Fargo' DVD, the Coens claim they were afraid nobody would have believed the crazy plot they came up with any other way.
The 2014 TV remake/spinoff/reinterpretation Fargo also claimed to be a true story, despite the two stories being set in the same place in different decades, with such a similar-but-markedly-different plot that they can't both have happened without someone mentioning it.