Caresse \c(a)-resse, car(es)-se\ as a girl's name is pronounced ka-RESS. It is of French origin, and the meaning of Caresse is "tender touch". See also Charis. Caresse has 3 variant forms: Caress, Caressa and Carressa. Baby names that sound like Caresse are Carisse, Carissa, Caresa, Charisse, Karisse, Cressa, Karessa and Karess.