Bohringer was born in Moulins, Allier, France, to a French mother, Huguette Foucault[3] and a German father.

Beginning in 1981 with the film Diva by Jean-Jacques Beineix, he followed with numerous other roles, winning two César Awards for L'Addition [fr] (1984) and The Grand Highway (1987).

Other notable performances include his work in Luc Besson's Subway (1985) and Gérard Jugnot's Une époque formidable... (1991).

He also became a favored actor for Jean-Loup Hubert, playing the flighty husband in J'ai épousé une ombre [fr] (1983), and a collaborator with Jean-Pierre Mocky and his friend Bernard Giraudeau.

This began a tour of more than two years, with Bohringer regaling the public with stories of alcohol, travel, Africa, women, and more.

In January 2013, he created the play J'avais un beau ballon rouge [fr], where he shared the stage with his daughter Romane for the first time.

In 2023, his daughter Romane put him onstage at the Théâtre de l'Atelier in Quinze rounds, a solo performance derived from his work of the same title.