Maurice Cossmann's father was an artist draughtsman and a talented lithographer.
His early education was at Condorcet College in Paris and he later gained the Diploma of the Central School of Arts and Manufacturing in the same city.
He was then employed by the Compagnie des chemins de fer du Nord.
Married and without a child, he loved to tell how the arrival of a small collection of fossils had led to his future studies of paleontology.
Certain of his works are still a major reference especially: Cossman published, sometimes collaboratively, 186 works (scientific papers and monographs) between 1879 and 1926 and he was the Editor of Revue critique de paléozoologie et de paléophytologie Paris 1897–1919.