Will Smith Goes Chic Shopping with the Family in Capri, Italy

Will Smith doesn't travel lightly when he does Italy -- he brings the whole fam along for the ride ... and makes sure their threads are up to par.

Will was out and about in Capri Tuesday with Jada Pinkett Smith, their two kids Jaden and Willow ... as well as his other kid from his first marriage, Trey. They were shopping at Autori Capresi -- a high-end fashion boutique well known to locals.

You can tell how serious everyone's taking their new duds -- not a whole lot of smiles here inside the store ... except for Will, of course, who was smiling from ear to ear.