The actor and supermodel are floating around the Mediterranean on a big boat ... lathering each other up with sun tan oil and packing on the PDA with hugs and kisses.

Gigi and Bradley don't have the yacht all to themselves though ... his 7-year-old daughter Lea De Seine was onboard too ... Bradley co-parents her with Russian model Irina Shayk.

The three amigos shared a banana boat ride together, with Lea up front, Gigi in the middle and Bradley acting as the caboose.

Bradley soaked up the sun in some olive green swim trunks and Gigi showed off her runway-ready figure in a skimpy black and white bikini.

There were a few smooches and warm embraces on the deck ... but they didn't go full "Titanic."

The couple tooled around in a smaller boat too, and Gigi took a dip to cool off.