Fire in the Flesh(1958)

Physicist Theodore Heldt, his young daughter Fern and his assistant Larry Gordon, on board a ship for a scientific expedition, are shipwrecked in the Pacific Ocean after a terrible storm. They find themselves safe and sound on an exotic desert island paradise. Several years pass, the professor dies and Fern and Larry, long in love and alone in the world, are united. One day, the ship they'd been waiting for appears, but the sailors are three smugglers who, instead of representing salvation, pose a threat to the young couple.