If the goal is to translate "I have a pet", then j’ai un animal de compagnie is a correct translation while j’ai un animal alone doesn’t necessarily mean it is a pet.

pet

animal

An animal de compagnie (pet) is the animal who keeps company with his owner hence compagnie also called animal domestique, where domestique is the adjective of domicile meaning a house whether it means a flat or a farm or any kind of living arrangement. Whereas an animal is just that, it could be wild, dangerous, not necessarily living in your home and keeping you company.

Note that in English, and in the US in particular, a pet is sometimes called a "companion animal," which would seem to be a direct, literal translation of "animal de compagnie."