Choquet was born in Solesmes, Nord. His contributions include work in functional analysis, potential theory, topology and measure theory. He is known for creating the Choquet theory, the Choquet integral and the theory of capacities.
He did postgraduate work at the École Normale Supérieure Paris where his advisor was Arnaud Denjoy. He was Professor at the University of Paris (subsequently Paris VI) from 1940 to 1984 and was also Professor at the École Polytechnique from 1960 to 1969. His honours and awards included being a Member of the Académie des Sciences, and an Officier of the Légion d’Honneur.
He was married to mathematician and mathematical physicist Yvonne Choquet-Bruhat. He died in Lyon in 2006.