Waldschmidt was educated at Lycée Henri Poincaré and the University of Nancy until 1968.
In 1972 he defended his thesis, titled Indépendance algébrique de nombres transcendants (Algebraic independence of transcendental numbers) and directed by Jean Fresnel, the University of Bordeaux.
He became a lecturer at the University of Paris VI (Pierre et Marie Curie) and then became a professor there in 1973.
Waldschmidt was also a visiting professor at places including the École normale supérieure.
In 2021, he was awarded the Bertrand Russell Prize by the American Mathematical Society.