I think the best "foodie" lunch on the island is Bacchus (also a high end wine shop + deli type store) in Hope Estate

https://bacchussxm.com/en/saint-martin-en/

Hope Estate also has a nice large grocery store called Super U, where you can purchase all sorts of French stuff (is a large chain in France).

https://www.magasins-u.com/magasin/superu-saintmartinhopeestate