I second the suggestion of Super U because you're staying in or near Grand Case. There's one in Marigot (on the way to GC) in the Howell Shopping Center located just past the athletic field on right coming from airport area. (or on left if coming from Grand Case area).

I heard this market opened another location between Grand Case and Orient near Hope Estate.

When we stay on the Dutch side we no longer shop at Grand Marche. Instead we stop at Fresh Market in Phillipsburg area before Madam Estate on way to the zoo. Best vegetables & fruits.