The island of Noirmoutier without a car is a great way to enjoy the island in complete peace of mind!
Getting to the island of Noirmoutier from Paris: from Gare de Montparnasse station, book a Paris-Noirmoutier journey (with a connection in Nantes) on https://www.sncf-connect.com/en-en/. Your train stops at Nantes station. Go to the Nantes bus station (south exit of the SNCF station) to board a coach (Aleop line 13 Nantes - Fromentine - Noirmoutier).
Getting to the island of Noirmoutier from Nantes: book a Nantes-Noirmoutier journey on https://www.sncf-connect.com/en-en/. From the Nantes bus station (south exit of the SNCF station in Nantes), board an Aleop coach line 13 "Nantes - Fromentine - Noirmoutier".
Getting to the island of Noirmoutier from La Roche-sur-Yon: from La Roche-sur-Yon station, take a Vendexpress La Roche-sur-Yon - Challans bus. When you arrive at Challans station, go to the bus station to board an Aleop/Sovetours coach, route 571.
Getting to the island of Noirmoutier from Challans: from Challans station, board an Aleop/Sovetours coach, line 571.