Couppey was born in Paris. He studied at the Paris Conservatoire with Victor Dourlen. At the age of 17 he became an assistant professor of harmony, receiving the first prize in pianoforte and harmony in 1825, and in pianoforte accompaniment in 1828. In 1837, he became professor of solfège, succeeding Henri Herz and Victor Dourlen in harmony and accompaniment in 1843. From 1854 to 1886, he taught piano and wrote a larger number of textbooks for the instrument such as École du méchanisme du piano, 24 Études primaries, and Cours de piano élémentaire et progressif. Among his pupils were the singer Édouard Batiste, the composer Émile Jonas and the pianists Mathilde Bernard-Laviolette, Cécile Chaminade, and Henri Verley.