Preheat a grill to medium heat.
1) Combine the vinegar, a splash of water, the shallots, mustard, mayonnaise and tarragon in a blender and puree until smooth. With the motor still running, slowly pour in the oil and blend until the vinaigrette has emulsified. Adjust the seasoning with salt and black pepper, to taste.
2) Brush the potatoes with some rapeseed oil and season them with salt and black pepper, to taste. Grill them, cut side down, until they are lightly golden, then turn them over and continue grilling until they are just cooked through. Transfer them to a platter and immediately drizzle with the vinaigrette.
Garnish with a few tarragon leaves and serve.