The Light Between Oceans (2016) on Netflix

Tom, a war weary man takes a job as a lighthouse keeper on an island for the solitude. He meets a beautiful young woman, Isabelle and they eventually marry. One day they see a small dingy with an infant and man inside floating in the ocean. They rush to rescue them only to find the man is dead. They struggle over the decision to report it and whether to keep the baby. Heartbroken because she had already had miscarriages twice, Isabelle persuades Tom not to tell anyone about this and leave the girl to herself as if it were their child. He buries the man on the island, and the couple names the girl Lucy. He succumbs to her persuasion just to make her happy. It's only years later that they discover that the child still has a mother looking for her.