The following definition gives the essential meaning of this word.

(TLFi) II B. − Usuel, emploi adj. Bête féroce, de pelage fauve et souvent de grande taille (félin généralement).

However in the context of hunting (rarely found in comparison) this word comes to have a different meaning; it is used to differentiate brown coloured four-legged game from black.

(TLFi) II A. − VÉN., vx, emploi adj., gén. au plur. Bêtes sauvages de pelage fauve (cerfs, daims, etc.), par opposition aux bêtes noires* et aux bêtes rousses*.

The meaning "wild cat" must be rare; it is not found in the TLFi and I never found it myself. "Wild animal" is not correct; only a wild animal of the big cat sort can be called a "fauve".

Fauve as a noun is nowadays exclusively to name big wild cats (Lions, tigers, panthers, cheetahs and the likes), not to name any other kind of wild animal.

As an adjective, fauve is the name of a group of colors (English fulvus), from the Latin flavus.

Naming animals from that adjective came later, and the link between the color and the animal is weak (a black panther is still a fauve).