Pet

de compagnie

(kept or treated as a pet)

fétiche

(favourite; cherished)

animal de compagnie

(an animal kept as a companion)

animal domestique

(an animal kept as a companion)

animal familier

(an animal kept as a companion)

chouchou

(person or animal especially cherished)

caresser

(fondle (an animal))

peloter

(fondle (another person) amorously)

se peloter

(intransitive: fondle amorously)