Couette was born in Tours, France, as the only child of Alfred Ernest Couette, a cloth merchant.
Finishing his education with the Frères des Écoles Chrétiennes he obtained a baccalauréat in humanities and in science, both in 1874, as well as bachelor's degrees in mathematics and physical science (delivered by the Faculté de Science in Poitiers) in 1877 and 1879 respectively. Following a short spell as a lecturer in Angers, he joined the 12th Artillery Regiment at Vincennes for one year of voluntary military service.
In 1881 he settled in Paris and enrolled in the Sorbonne, studying physical science in preparation for the agrégation, a French teaching diploma. Couette later taught in Arcueil and the École Sainte-Geneviève in Paris. At the Sorbonne he studied under Joseph Boussinesq and from 1887 onwards worked at the Physics Research Laboratory under Gabriel Lippmann( who would later receive the Nobel Prize in Physics). Couette also took his doctoral degree on the friction of liquids ("Studies on the Friction of Liquids", Etude sur le frottement des liquides, Gauthiers-Villars 1890).
Soon afterwards he was given a professorship of physics at the Catholic University of Angers (now known as Université Catholique de l'Ouest) as well as other teaching commitments such as at the Free Faculty of Science, the School of Agriculture and several secondary schools in Angers.
Couette was a member of the French Physics Society and retired in 1933.
