The youngest of fourteen children in a poor family from Etampes in France, Geoffroy was supported by the local clergy, who recognized his precocious intelligence. He took a scholarship to the Collège de Navarre, Paris, and was soon appointed as a demonstrator at the Jardin des Plantes, a precursor of the Muséum National d'Histoire Naturelle, as his predecessor, Bernard Lacépède, fled the Revolution. In 1793 Geoffroy became professor of vertebrate zoology at the museum; the comparable chair of invertebrate zoology was held by Lamarck.

In 1798 Geoffroy accompanied Napoleon on his conquest of Egypt and contributed to the celebrated 24 volumes of the Description de l'Egypte (1809–28; Description of Egypt). He traveled as far down the Nile as Aswan and while in Egypt he examined a number of mummified cats taken from ancient tombs. They were, he noted, identical to the animals of his day. Did this mean that species were fixed? If they were fixed why were there so many similarities between different forms? Why, for example, despite differences in external form, do the skeletons of bats, whales, and dogs resemble each other so closely?

Geoffroy derived his answer from German Naturphilosophie (nature philosophy), which claimed to see beneath an apparent diversity of form, mere variations on a single plan. There was a vertebrate type which could be identified in all vertebrates. Thus he demonstrated in 1807 that pectoral fins in fish and the bones of the front limbs of other vertebrates were morphologically and functionally similar.

But Cuvier had identified in the operculum, a bony flap covering gill slits in fishes, an apparently unique structure. It took Geoffroy a decade's investigation before he could explain it away as equivalent to the auditory bones in mammals. He was thus able in his Philosophie anatomique (1818; Anatomical Philosophy) to announce the principle of anatomical connection claiming that the same anatomical structural plan could be identified in all vertebrates.

By 1830 Geoffroy had begun to argue that there was a universal “unity of composition,” quoting in evidence work claiming to have detected a unity in crustacea, fish, and mollusks. Such views brought a savage onslaught from Cuvier who insisted that there were distinct forms in nature, and that parts were formed to meet functional needs.

But, once having accepted a unity of composition, it becomes possible to see how one species can be transformed into another. If birds and reptiles are built to the same plan, then “an accident that befell one of the reptiles…could develop in every part of the body the conditions of the ornithological type.” Geoffroy was thus moving late in his career to some form of evolutionary theory. A stroke in 1840 which left him blind and paralyzed brought such work to an end.

Geoffroy was succeeded at the museum in 1841 by his son, Isidore (1805–61), also a distinguished biologist and best known for his three-volume work on teratology, Histoire…des anomalies de l'organisation chez l'homme et les animaux (1833–37; Account…of Irregularities in the Structure of Man and the Animals).