My friend Thierry Benissa, who used to manage the beach at Club O, God rest his soul, used to fish off the rocks in Marigot harbor. Of course there's a fairly new marina (Marina Fort-Louis) there now. But I believe the stone jetty is still there.
From the road that runs closest to the water head north till you hit Rue De La Republique, go left passed Fort Louis and you will hit Boulevard Du Docteur H. Petit. You should see the jetty on your left.
Jetty fishing can be dangerous but Thierry said there are fish there.
I might also suggest getting a map of SXM from one of the TTOL sponsors in case someone else tells you of other places. It's great!
I looked at the sponsor list and I don't see the ad, but you can order a map on Amazon.