French painter Michel Marnet (Charles Boyer) meets American singer Terry McKay (Irene Dunne) aboard a Ocean liner crossing the Atlantic Ocean. They are both already engaged, he to heiress Lois Clarke (Astrid Allwyn), she to Kenneth Bradley (Lee Bowman). They begin to flirt and to dine together on the ship, but his notoriety and popularity on the ship make them conscious that others are watching. Eventually, they decide that they should dine separately and not associate with each other. At a stop at Madeira, they visit Michel's grandmother Janou (Maria Ouspenskaya), who approves of Terry and wants Michel to settle down.