Roche studied at the university in his native city of Montpellier, obtaining his doctorate there in 1844. After further study in Paris he returned to Montpellier in 1849 and served as professor of pure mathematics from 1852 until his retirement in 1881.

Roche's name is still remembered by astronomers for his proposal in 1850 of the limiting distance since named for him. He calculated that if a satellite and the planet it orbited were of equal density then the satellite could not lie within 2.44 radii, the Roche limit, of the larger body without breaking up under the effect of gravity. As the radius of Saturn's outermost ring is 2.3 times that of Saturn it was naturally felt that the rings could well consist of broken-down fragments of a former satellite that had transgressed the forbidden limit. It is now thought, however, that the Roche limit has prevented the fragments from aggregating into a satellite.

Roche later worked on the nebular hypothesis of Pierre Simon de Laplace, submitting it to a rigorous mathematical analysis and concluding in 1873 that a rapidly rotating lens-shaped body was in fact unstable. He also published work on the structure and density of the Earth and produced a generalization of Taylor's theorem, much used in mathematics.