If you're using the walnuts, place in a hot oven (about 200C/400F/Gas 6) for a few minutes until beginning to colour slightly. This gives a fresher, less bitter flavour to the nuts.
Place the vinegar, mustard, oils, honey and salt and pepper in a screw-top jar or in the bowl of a small hand blender. Shake or blend well until creamy. Add more seasoning if preferred.
Cook the potatoes in boiling salted water for about 15-20 minutes until just tender. Drain well and, when just cool enough to handle, cut into halves or quarters, if quite large.
Place the potatoes in a mixing bowl with the tarragon, shallots, cornichons or gherkins and walnuts, if using, and toss in as much or as little of the dressing as you want. Serve just warm or, if you're not eating straight away, refrigerate and return the salad to room temperature before eating.