The sentence in French would seem rather cumbersome, because the "official name" of Jersey Shore in French es "la rive (or, les rives) du New Jersey." So, in order not to repeat "New Jersey" twice, I would probably just say "J'habite sur la rive du New Jersey." Caveat: I speak intermediate French. I am not a native speaker. Native speakers: please chime in!!!

J'habite dans le New jersey plus précisément à Jersey shore