His contributions include work in harmonic analysis and differential equations.

Denjoy was an Invited Speaker of the ICM with talk Sur une classe d'ensembles parfaits en relation avec les fonctions admettant une dérivée seconde généralisée in 1920 at Strasbourg and with talk Les equations differentielles periodiques in 1950 at Cambridge, Massachusetts.

In 1931 he was the president of the Société Mathématique de France.

In 1942 he was elected a member of the Académie des sciences and was its president in 1962.

He was an atheist with a strong interest in philosophy, psychology, and social issues.