Place the potatoes in a large pot and fill with enough water to cover. Bring to a boil with the pot uncovered, then remove from the heat, cover and let stand for 25 minutes. Drain and transfer to a serving bowl. Stir in the French salad dressing while the potatoes are still warm. Cool for at least 1 hour.
Add the celery and green onions to the potatoes and mix in the mayonnaise, sour cream, mustard, mint, dill and pepper. Refrigerate until serving.