Position a rack in the middle of the oven and preheat to 400 degrees.
Wrap the beets tightly in a packet of aluminum foil. Set directly on the oven rack and bake until very tender, 1 hour to 1 hour and 15 minutes. Remove from the oven and cool the beets in the foil to room temperature. The beets can be prepared to this point up to 1 day in advance. Refrigerate them in their foil, returning them to room temperature before proceeding. Peel the beets and cut them into eighths.
On a sheet pan, toss the potatoes with the oil. Season lightly with salt and pepper. Toss the potatoes, stirring them occasionally, until they are tender and well browned, 30 to 40 minutes. Remove from the oven and cool.
Bring a medium pan of water to a boil. Add the artichokes and 2 teaspoons salt and cook uncovered, stirring occasionally, until tender when pierced with a fork, about 15 minutes. Drain well and cool. Quarter the artichokes vertically.
Bring a large pot of water to a boil. Add the haricots verts and 2 teaspoons salt. Cook until just tender, 2 to 3 minutes after the water returns to a boil. Drain the haricots verts, immediately transfer them to a bowl of iced water and let stand just until cool. Drain well.
Prepare a hot charcoal fire or preheat a gas grill to medium high. When the fire is hot, distribute the wood chips if you are using them. Position the grill rack about 6-inches above the heat.
Spread one side of the tuna with half the tapenade. When the fire is hot, lay the fish on the rack, tapenade side down. Cover and grill for 4 minutes. Spread the upper side of the tuna with the remaining tapenade. Turn the fish and grill another 3 to 5 minutes for medium rare, or until done to your liking. Transfer to a cutting board and cool slightly. Remove and discard the skin and cut the tuna into slices that are 2-inches long and about 1/2-inch thick. Season generously with freshly ground pepper.
In a medium bowl, toss the artichokes with 1 tablespoon of the vinaigrette. In a second bowl, toss the potatoes with 2 tablespoons of the vinaigrette. In a third bowl, toss the beets and red onions with 2 tablespoons of the vinaigrette. In a fourth bowl, toss the tomatoes with 2 tablespoons of the of the vinaigrette. Season each vegetable to taste with salt and pepper and marinate for 30 minutes.
Mound the mesclun in the center of a large platter. Spoon the marinated artichokes, potatoes, beets, and tomatoes around, not on, the mesclun. Add the hard cooked egg wedges to the platter and drizzle them with a tablespoon or two of vinaigrette. Arrange the tuna slices over the mesclun and drizzle the fish with 3 tablespoons of vinaigrette. Scatter the olives and arrange the caper berries decoratively over and around the various components and serve immediately. Pass the remaining vinaigrette at the table.
In a medium bowl whisk together the vingar, mustard, shallot, hot pepper sauce and salt. Continue to whisk while adding the oil in a slow stream; the dressing will thicken. Add freshly ground pepper to taste and adjust the seasoning. Use within an hour or so of completion.