There is a beach bar on Le Galion that rents chairs. If you're not familiar with the island, I would suggest taking the route through Marigot.

From SBR, head back toward the airport. At the roundabout at end of the runway, take the causeway across the lagoon. Turn left at the end of the causeway and follow the main road through Marigot then through Grand Case and past the Orient Beach area. On your way through Marigot and Grand Case, you will encounter three roundabouts. Take the first exit out of each roundabout, which basically keeps you going the same direction you entered the roundabout.

There are a couple of gated entrances on the left to the Orient Beach area. After you pass those entrances (and a bit of winding), there is a left turn that has a sign for Club Orient and Le Galion. Turn left, and that road will take you past the famous Butterfly Farm and a horse stable to the beach area. The beach bar is to the left.

For what its worth, instead of the Marigot route, you could go through the counter-clockwise route through Philipsburg, but traffic is likely to be worse and there are a lot of turns. If you want to go that way, I would suggest scouting it out on Google Earth or Google Maps first.