I did some research on the holiday:
Nov. 11: St. Maarten Day. Public holiday. Parades and joint ceremony by French and Dutch officials at Border Monument obelisk commemorating long-standing peaceful coexistence of both countries. Tenth-annual 20-mile "Around the Island" race, based on historic folk tale about how the island's two-nation border was established. Also "St. Martin's Day," denoting start of "season."
French Side: Looks like everything
CAN be open. Plus they have an event in the French Quarter.
St Martin - French Quarters village day
Fun filled family day surrounded by the most popular traditional and cultural games and music.
Looks like those that were planning shopping in Philipsburg (Dutch side) will be disappointed.
This is a news story from November 2006:
PHILIPSBURG -The public is reminded that all stores have to be closed on St. Maarten/St. Martin Day, Saturday, November 11.
St. Maarten/St. Martin Day is an official holiday and, in keeping with the law on shop closure, all places of business have to be closed on that day, Lt. Governor Franklyn Richards stated in a press release on Monday.
No exemptions will be granted for business establishments to open on Saturday. This also includes stand-alone casinos, as well as casinos located on hotel properties with less than 200 rooms. Three cruise ships are scheduled to be in port on Saturday, but stores may not be open.
The law on shop closure makes a few exceptions. Pharmacies may be open, but only to sell medicines and medical products. Bars and restaurants, hotels and guest houses, stores located in hotels and on the airport and harbour premises, funeral parlours, gas stations, and bakeries selling pastries, milk and milk products also may open.