Jean Frenet entered École Normale Supérieure in 1840, then studied at Toulouse where he wrote a doctoral thesis in 1847. Part of the thesis contains the theory of space curves and contains the formulas now known as the Frenet-Serret formulas. Frenet gave only six formulas while Serret gave all nine. Frenet published this part of his thesis in the Journal de mathematique pures et appliques in 1852.
Frenet became professor at Toulouse, then in 1848 he was appointed professor of mathematics at Lyon. He was also director of the astronomical observatory there and, in this capacity, he conducted meteorological observations.
Frenet's exercise book on the calculus, first published in 1856 ran to seven editions, the seventh being published in 1917.