There are a lot of ways to adapt a film to a TV show, and it's not as common as it was for a while there. For a while, you had strange experiments like TV telling the story of Ferris Bueller, TV telling the story of Baby and Johnny from Dirty Dancing, and TV revisiting 9 to 5. Usually, it meant just moving the characters over to a series, having them played by new actors, and following new stories about them. (Melora Hardin as Baby Houseman!) Every now and then, it worked: you might have heard of M*A*S*H. Usually it did not: you might not have heard of The Firm, starring ... Josh Lucas. (Yes, a couple of those are also books. But ... still.)
It seemed, candidly, like an absurd idea when FX announced that it was making a TV series based on Fargo, the Coen Brothers film from 1996. That was a completed story that didn't lend itself to a lot of obvious "further adventures." It didn't seem like very much more activity could be ... afoot.
Furthermore, the film was full of performances surely no one would be dumb enough to try to do over, like Frances McDormand as Marge Gunderson and William H. Macy as Jerry Lundegaard. The Coens were on board as executive producers; what could these people possibly have in mind?
As it turns out, what they had in mind was a completely new story borrowing the tone, some of the dynamics, and some of the atmosphere of the film, but not the characters and not the story itself.