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Briot obtained a doctorate in March 1842 on the orbit of a solid body around a fixed point. He was professor at Orléans Lycée, then later at the University of Lyon. While there he met again his school friend Claude Bouquet with whom he did important work in analysis.
From 1851 Briot taught at various Lycées in Paris and he acted as substitute for courses in engineering, surveying, calculus, mechanics and astronomy at École Polytechnique and at Faculté des Sciences. From 1864 he was professor at the Sorbonne and at École Normale Supérieure.
He worked on analysis, heat, light and electricity. He wrote many important textbooks and received many honours for his work.
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