Are there ever any 5k or 10k or otherwise on the island? Search only turned up something about a beachball race at Club O. And that one looks a lot more fun anyway.
I have run 5K and 10K races on both sides of the island. To add onto satch74's suggestion, here is a list of upcoming races on Tri-Sport's web site: Tri-Sport Event Page. (Click on the Year's Planning tab.) For some races on the French side, a doctor's note certifying that you are in good condition is required.