The movie is inspired by real life events, the infamous Dupont de Ligonnès case, after Xavier Dupont de Ligonnès, the man who disappeared from his house in Nantes (in Northwestern France) in 2011, after killing and burying in his garden his whole family (his wife and their four children) as well as the two family dogs. By the time the bodies were found, he had already disappeared, and as of August 2024, he is still missing. In the movie, the killer is called Paul Bernardin.
On top of that, the story line of Michel Uzès in the movie, the man mistaken for Paul Bernardin, is similarly inspired by the story of Guy Joao, a retired man who was mistaken for Dupont de Ligonnès in Glasgow in 2019, and thus arrested and kept in jail for 26 hours, which sent the French media in a frenzy, with most newspapers the next day stating that the killer had been found. Like Michel Uzès, Guy Joao looked nothing like the killer, and wasn't the same height or age.
The title, "Les pistolets en plastique", meaning "Plastic pistols", conveys the idea that everything is fake in the movie: the detectives are fake, the real Bernardin is living under a fake identity, the wrong Bernadin is obviously not the real deal, even the cops involved are clearly not the sharpest ones. While reading his script again, writer/director Jean-Christophe Meurisse stumbled onto the scene where the star detective's children are playing with plastic pistols and so he knew he had found the title.