Carol, unfortunately most of the restaurants that fit your description ("high end French") are not open for lunch in GC. Like Le Cottage, L'Auberge Gourmande, Bistrot Caraibes, La Villa, Le Pressoir... they're only open for dinner as far as I know. Ocean 82, Nice SXM (as mentioned above), and Rainbow Cafe might be your few options. I doubt you'll find your souffle and you might find music you don't want (looking at you Rainbow haha).