It's caribbean... don't assume anything similar of what it would be like in the States... It may be not Claude, but as the oldest restaurant in Marigot they started as a simple "get together" table with homemade food, and nicknamed it the "Mini Club" as there was always only few people around, and mostly resident. It became more of a "restaurant" as to "our" standards much later.
Also, don't be mistaken by the position of the restaurant regarding to the water from the picture on trip-advisor... As I stated, marigot changed a lot in 30 years, as you did too.. ;-) (I still great!...LOL) Claude was right on the water until 1992... the waves were breaking bellow the deck of the restaurant. In 1992, the town and our "wonderful" politicians had the genius idea to gain land on ocean and they destroyed Marigot beach, killed ocean front businesses, filled up and extended the land surface area, to make a road and..... parking lot!.. yes.. parking lot on the water, with the most exclusive view....
I don't recall other restaurant or food place with a "man" or "person" name at that time beside Claude, except not on the water... there was a place called "Jean Dupond", but was an upscale type of restaurant and was on the Marina POrt La Royale in Marigot