Heaven Knows, Mr. Allison (movie, 1957)

In 1944, in South Pacific, the castaway Marine Corporal Allison drifts in a raft to the Tuasiva Island, where he meets Sister Angela. She tells him that she is the only person in the island and was left behind by the runaway boat to Fiji Island while seeking the local priest. Stranded in the island, but with water, fish and fruits, their paradisiacal life ends when the Japanese arrive to build a base, forcing Allison and the nun to hide in a cave. The crude marine provides the necessary supply for their survival and falls in love for the nun.