Steam the string beans until just crisp-tender. Cool them quickly in a bowl of ice water to stop the cooking, then trim as needed.
Bring a medium saucepan of lightly salted water to a boil. Add the potatoes and cook for 6 minutes, or until fork-tender.
Meanwhile, prepare the vinaigrette. In a small bowl, stir together the vinegar, lemon juice, mustard, garlic, tarragon, and salt and pepper to taste. Slowly add the olive oil, whisking until the mixture is well-blended.
Peel the cooked potatoes, if desired, and cut into ¼-inch slices while still very warm. Douse with 2 tablespoons of the vinaigrette and allow to cool.
Thoroughly wash and spin-dry the lettuce. Place in a large bowl, add 3 tablespoons of the vinaigrette, and toss lightly.
Place the lettuce on a platter. Arrange the string beans, potatoes, tuna, tomatoes, eggs, and bell pepper on top of the greens in a decorative fashion. Sprinkle the olives, capers, and anchovies over the salad, drizzle with the remaining vinaigrette, and serve.