If you chose the flight route to Paris, you can comfortably reach Arcachon by train to Bordeaux, then by local train directly to Arcachon. The Paris-Bordeaux trip will cost 60 EUR, with a travel time of 3.5 hours. Then from Bordeaux station, a local train will take you to Arcachon in 52 minutes and 15 EUR.
If you fly to Bordeaux airport, you will need to take a bus to the city near Hall B, go to Bordeaux station and from there take a train to Arcachon.
You can also take a cab in Bordeaux or rent a car. It should be noted only that such a trip will cost you much more.
