He was born in Rouen, the son of naturalist Félix Archimède Pouchet (1800–1872). In 1865 he became chief of anatomical work at the Muséum national d'histoire naturelle in Paris, and was later co-director of the maritime laboratory at Concarneau. From 1879 to 1894 he was professor of comparative anatomy at the Muséum national d'histoire naturelle. In 1892 he was part of an early scientific polar expedition to Svalbard and Jan Mayen.
Pouchet made contributions in several scientific fields, and specialised in comparative anatomy of fishes and whales. He was a prime advocate of polygenism, and was the author of an anthropological work titled De la Pluralité des races humaines (1858), which was translated into English as The Plurality of the Human Race in 1864 by the Anthropological Society.
- De la Pluralité des races humaines, 1858
- Journal de l’anatomie et de la physiologie (Journal of anatomy and physiology), with Charles-Philippe Robin (1821–1885), 1878
- Mémoire sur le grand fourmilier (Discourse on the giant anteater), 1874
- Precis d'histologie humaine et d'histogénie (Treatise of histology and human histogeny), with Frédéric Tourneux (1851–1922), 1878
- La Biologie aristotélique (Aristotlean biology), 1885
- Rapport sur le laboratoire de Concarneau (Report on the laboratory at Concarneau), 1888
- Traité d'ostéologie comparée (Treatise of comparative osteology), with H. Beauregard, 1889.
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