Nickie Ferrante (Cary Grant), a well-known Playboy lifestyle, meets Terry McKay (Deborah Kerr) aboard the transatlantic ocean liner en route from Europe to New York. Each is involved with someone else. After a series of meetings aboard the ship, they establish a friendship. When Terry joins Nickie on a brief visit to his grandmother Janou while the ship is anchored near her home at Villefranche-sur-Mer on the Mediterranean coast, she sees Nickie with new eyes and their feelings become deeper. During their visit, Janou tells Terry that Nickie is a talented painter but destroys most of his paintings because they don't meet his standards. As the ship returns to New York City, they agree to reunite at the top of the Empire State Building in six months' time if they have succeeded in ending their relationships and starting new careers.