A monkey (le singe) is classified as a wild animal (un animal sauvage). Monkeys live naturally in forests, jungles, and savannas, and are not domesticated animals raised by humans for agricultural or companion purposes.
The other classifications do not apply:
aquatique (aquatic) - Monkeys are not water-dwelling animals. Aquatic animals include fish, dolphins, and whales.
volant (flying) - Monkeys cannot fly. Flying animals include birds, bats, and certain insects.
domestique (domestic) - Domestic animals are those bred and kept by humans, such as dogs (chiens), cats (chats), cows (vaches), and chickens (poules). While some people keep monkeys as pets, monkeys are fundamentally wild animals by biological classification.
In French vocabulary, the distinction between sauvage (wild) and domestique (domestic) is commonly tested. Wild animals live freely in nature; domestic animals are raised and depend on humans.