Boil the potatoes, ideally with their skins on, in a large pan of well-salted water for about 6 minutes. Then take the pan off the heat and leave the potatoes to stand in the cooking water, covered, for about 15 minutes - depending on their size. Cooking the potatoes this way gives them a pleasantly firm texture and ensures they do not fall apart. Test with a skewer that the potatoes are tender before draining off the water.
Peel the potatoes and cut them into bite-sized pieces.
Stir the crème fraîche, mayonnaise, shallots, tarragon and white wine vinegar together well, and season to taste with salt and freshly ground pepper.
Fold the potatoes into the dressing and refrigerate the salad until ready to serve.