He studied from 1989 to 1993 at the École normale supérieure de Cachan, and then moved to the University of Paris-Sud, where he earned a doctorate in 1995 under the supervision of Étienne Fouvry and then a habilitation in 1998.
He was a professor at the University of Montpellier from 1998 to 2008, when he moved to École Polytechnique Fédérale de Lausanne. In 1999, Michel was awarded the Peccotand gave the fr:cours Peccot at the Collège de France. In 2006, he was an invited speaker at the International Congress of Mathematicians. In 2011, he was elected to the Academia Europaea.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.