No, Fargo is not a true story. It's a fictional crime drama.
Fargo is purely fictional. The plot and characters were created for the movie and don't have real-life counterparts. But it does a great job of creating a believable and engaging story within its fictional framework.
Fargo isn't based on real events. It's the imagination of the filmmakers. However, it's so well-written and directed that it can feel almost real at times despite being completely made up.