In Celtic, name Alain means – Variant of Alan: Harmony, stone, or noble. Also fair, handsome. Originally a saints name, it was reintroduced to Britain during the Norman Conquest, remained popular throughout the Middle Ages, and was revived in the 19th century.. Other origins for name Alain include – Celtic, French, French, Gaelic, English. Name Alain is most often used as a boy name or male name.