He was the son of mathematician Joseph Louis François Bertrand (1822–1900), and son-in-law to physicist Éleuthère Mascart (1837-1908).

He studied at the École Polytechnique, and beginning in 1869 he attended the Ecole des Mines de Paris.

Bertrand, a founder of modern tectonics, originated an orogenic "wave theory" of mountain-building and introduced[when?]

His wave theory described a build-up of massive folds of earth taking place over successive geological eras, called the Caledonian, Hercynian and Alpine periods of orogeny.

Bertrand later added a fourth event called the Huronian orogeny, which took place 2400 to 2100 million years ago, in Precambrian time.