You really have two choices for lunch on the beach: wild, hedonistic, loud (and probably vulgar) beach club with DJ, spraying of champagne, and people who use their money to give themselves some feeling of importance, OR Bambou and company where you are on the beach but can enjoy the food you have ordered. Service tends to be fairly punctual and attentive, prices are OK but on the high side, and food is good to very good, so end result is you can be quite satisfied. Bambou is, with Club 55, probably the best bet for an adult lunch with good food and fun atmosphere, without the wild party scene of places like the Voile Rouge. Try the red Sancerre cold and the fish grilled.
Not much unless you want to plant palm trees and create waves, but then you'd be better off in Brazil. Pimm's are better at Glyndebourne.