Meaning uncertain, possibly a derivative of
Anne 1 or
Agnès. It was used in Jean-Henri Guy's opera
Anacréon chez Polycrate (1798), where it is borne by the daughter (otherwise unnamed in history) of the 6th-century BC tyrant
Polycrates of Samos. Guy could have adapted it from a classical name such as
Anaitis or
Athénaïs.
A famous bearer was the Cuban-French writer Anaïs Nin (1903-1977), known for her diaries.