Set the potatoes in a large (6-quart) pot, cover them with cold water by a couple of inches, stir in 2 Tbs. salt, and bring to a boil. Reduce the heat to a gentle simmer, cover, and cook until the potatoes are tender when pierced with a fork, about 10 to 12 minutes. Stir in the haricots verts and cook until they turn bright green and tender, about 3 to 4 minutes. Drain well and cool under running water.
In a blender or food processor, blend the vinegar with the mustard. With the machine still running, add the oil in a slow, steady stream so the mixture comes together into a thick emulsion. Add the shallot, 2 tsp. thyme, 1 tsp. salt, and 1 tsp. pepper, and purée until incorporated. Taste and season the dressing with more salt and pepper if needed. Add 1 or 2 Tbs. water if needed to thin the dressing to a pourable consistency. Transfer the potatoes and beans to a large mixing bowl and toss well with half the vinaigrette. Taste and season with salt and pepper if needed and transfer to a large platter. In the same mixing bowl, toss the tuna with the capers and 2 or 3 Tbs. of the vinaigrette, and set them over the potatoes in the center of the platter. Sprinkle the tomatoes and olives over the potatoes, around the perimeter of the tuna. Drizzle the salad with the remaining vinaigrette, sprinkle with the remaining 1 tsp. thyme, and serve.
To plate individually, lightly toss the potatoes, beans, tomatoes, and olives with half the vinaigrette and plate; top with the tuna, capers, and the remaining thyme; and serve the remaining dressing on the side.
With a loaf of good French bread, the salad is meal in and of itself; ending with Blueberry-Cassis Fool makes it a meal to remember.