Cover potatoes with cold water in a large saucepan. Add 1 tsp. salt, cover and bring to a boil. Uncover, reduce heat and simmer until tender but not mushy, 10 to 12 minutes. Drain, then place in a bowl of ice water to stop cooking. Drain again. Cut each potato in half, or into quarters if they're larger.
Bring another large saucepan of water to boil, add beans and 1 tsp. salt, and cook until just tender, 3 to 4 minutes. Drain, plunge into ice water and drain again.
Make dressing: Whisk together mayonnaise and vinegar in a medium bowl. Stir in scallions, parsley, tarragon, 1/2 tsp. salt and pepper to taste.
Combine potatoes, green beans and dressing in a large salad bowl and toss gently to coat, being careful not to break up potatoes. Refrigerate for at least 1 hour, and up to 1 day, before serving to allow flavors to blend thoroughly.