Here is info from a travel web site regarding shops on St. Marten:
What are the Business Hours on the island?
Stores in Philipsburg are open all day Monday through Saturday, and some are open on Sunday if there is a cruise ship in port. In Marigot, the shops tend to close between noon and I p.m. and reopen at 3:00 p.m. until the late afternoon or early evening. Most businesses are closed on Sunday, and so are many restaurants. Grocery stores are open Monday - Saturday 8:00a.m. - 8:00p.m., Sunday 9:00a.m. - 1:00p.m. To make the most of your day, YOU should plan your activities accordingly.