Production Studio
Ethan Coen/Polygram Filmed Entertainment, Working Title Films
Bad as They Wanna Be
The Coens didn't only write and direct Fargo; they also produced it.* Yep, we've got ourselves a triple threat. (*Yeah, we know that Ethan Coen is credited as the producer, but it's always a joint effort with the bros.)
Unless you consider the fact that they edited it (under a pseudonym), which makes them more like a quadruple threat.
The Coen brothers do their own thing. They're not interested in churning out flicks with mass appeal consisting solely of highly orchestrated car chases or whatever. They're committed to delivering their full, unadulterated Coen magic. Quirky characters? Check. Flashes of odd violence? Check. Investigations into The Absurd? Check.
Complete Control
In producing their own film, they managed to retain total creative control and make exactly the movie they wanted to make. And they've continued doing this: Fargo is as distinct a Coen work as later movies like The Big Lebowski (1998), Burn After Reading (2008), and Inside Llewyn Davis (2013). Which is not to ignore the epic, Oscar-winning masterwork, No Country for Old Men from 2007, but that was an adapted screenplay based on a Cormac McCarthy book, and not an original Coen story.
There wasn't the kind of production struggle that Francis Ford Coppola had to endure when making The Godfather. Instead, the Coens had the kind of creative control that Orson Welles had when making Citizen Kane (the one time Welles was afforded full creative control, incidentally). This definitely shines through in the film. Fargo isn't really similar to anything that had come before it.
Undoubtedly, this is partly thanks to the fact that there was no producer hissing into Ethan Coen's ear, "What's with these accents? We should change the setting to New York." They were able to explore the world they knew and make something truly original.
Even though Fargo's a pure slice of Minnesota and North Dakota, the companies that helped produced it were actually British. One of these guys was Polygram Filmed Entertainment, which no longer exists, and is known for producing Hugh Grant movies like Four Weddings and a Funeral and, later, Notting Hill. The other was Working Title Films, which had already produced the Coens' Cannes-dominating Barton Fink. In fact, Working Title continued working with the Coens' up until recent years, co-producing A Serious Man in 2009.