There is lots of surfing in FP, lots of surfing culture.
Body surfing at the Radisson hotel is definitely a possibility, I've seen the local kids doing it, or on boogey boards. But the real surfing takes place further out, outside of the lagoon, on Moorea, Raiatea, etc., so I think if you wanted to do that, you'd have to find somebody to take you out past the lagoon.
I just did a search over at tahiti-explorer.com, on "surfing", and some hits, so you could do the same. One theme is that renting boards is difficult, so you might have to bring your own, which may not be an option!
Oh, I have also seen kite boarding several times, both on Moorea, and between Raiatea and Taha'a. Now that looks like an exciting sport!