After studying advertising at the Duperré School of Applied Arts in Paris, Beauchard began working in comics in 1985 (Pas de samba pour capitaine Tonnerre), and wrote and illustrated stories in numerous magazines, including Okapi, À suivre, Tintin Reporter, and Chic.

In 1990, he co-founded the independent publisher  L'Association, which became a major force in French small-press comics. His comics appeared in the L'Association anthology magazine Lapin and in numerous small-format books. Much of his work in the 1990s was dream art, collected in le Cheval blême and les Incidents de la nuit.
From 1996 to 2003, he created the acclaimed six-volume autobiographical epic l'Ascension du Haut Mal (meaning, literally, "The Rise of the High Evil" but published in English as Epileptic, "haut mal" indicating what is referred to in English as a grand mal seizure). It was the first of his long works to be translated into English, and is now considered to be among the masterpieces of recent Franco-Belgian comics. The series has been repeatedly nominated for prizes at the Angoulême International Comics Festival: in 2002, the fourth volume received the Angoulême International Comics Festival Prize for Scenario and in 1998 and in 2004, volumes 2 and 6 were nominated for the Prize for Best Comic Book.
Since 1997, he has also worked for publishers other than L'Association, and has collaborated with other authors such as Joann Sfar, Christophe Blain, and Emmanuel Guibert.
In 1998, he was named European Cartoonist of the year by The Comics Journal.
In 2005 Beauchard was awarded the Ignatz Award for Outstanding Artist.
With historical assistance by Jean-Pierre Filiu, Beauchard published the 2012 graphic novel Best of Enemies: A History of US and Middle East Relations through SelfMadeHero. It was translated to English by Edward Gauvin.