The Pont de Ré connects the island to La Rochelle. There is a toll for cars crossing to the island (free on the return). La Rochelle itself has a TGV station with direct trains from Paris Montparnasse, and the airport has seasonal flights.
Buses run from La Rochelle to the main villages on the island. In summer, leaving your car on the mainland and cycling across is a pleasant option — and avoids the congestion on the bridge.