(At around 20 min.) In Manu's trailer, Adrien has a glass that seems to be half full of red wine, with the bottle apparently about 1/3 full of red wine next to him. When he pours himself a refill, what comes out is clearly water.
In one of the first sequence you can see slightly blurred in the background the logo LCL (yellow letters on a blue background) of the Crédit Lyonnais bank. The LCL name/logo was only introduced around 2005 and there did not exist yet in 1984.
In a hospital scene towards the end of the film, the pillow behind the actor's head reads "HOPITAUX DE PARIS 2006" on the design in numerous places, though the film was supposed to be shot in the 80s.
In some scenes in the streets of Paris, you can see a couple Renault Twingo parked by the sidewalk. This model was first introduced in 1993.
In several scenes, Paris métro signs (at tabacs and on buses) sport the green logo that wasn't introduced until 1992. In 1984/85, the tickets and logo should have been yellow.