He was the son of Simon Marie (1775–1855) an infantry captain in Napoleon's Grande Armée from a modest background, and Henriette Josephine de Ficquelmont (1780–1843), poor, but from the nobility of Lorraine.

In 1862, backed by the famous mathematicians Joseph Liouville and General Jean-Victor Poncelet, Maximilien Marie was appointed professor of Mechanics at the École Polytechnique.

Besides his academic achievements at the Polytechnique, he wrote the book Théorie des fonctions de variables imaginaires relating to the Imaginary unit.

He published a 12-volume encyclopedia, History of the Mathematics,[8] which was divided into two parts: Théorie des fonctions de variables imaginaires (tomes I à III, Gauthier-Villars, 1874–1876, 3 vol.)

He had one elder sister, the famous positivist muse Clotilde de Vaux, and one younger brother, Léonard Marie (1820–1860), chevalier of the Légion d'honneur, who was also a military officer trained at the École Polytechnique and who died without issue at the Battle of Palikao.