Many people will think of the current pop superstar Ariana Grande when they hear this name. But this is different version that feels french (Ariana feels more Spanish). Quite rare in English speaking countries.
Ariane is the French form of the Greek Ariadne. In Greek mythology, Ariadne was the daughter of King Minos. She fell in love with Theseus and helped him to escape the Labyrinth and the Minotaur, but was later abandoned by him. Eventually she married the god Dionysus.