Boil the potatoes until fork tender, about 12–15 minutes. Drain and let cool slightly.
Blanch the green beans for 2–3 minutes until bright green and slightly tender, then drain.
Whisk together the Dijon mustard, lemon juice, water, salt and black pepper until smooth.
Toss the potatoes and green beans with the dressing, then finish with the fresh parsley and chives.
Serve slightly warm or chilled.