Step 1Combine the shallots, capers, cornichon, mustard, vinegar, oil, egg white, egg yolk, tarragon, parsley, chives and salt and pepper to taste in a small mixing bowl or lidded jar. Whisk or shake well to blend into a smooth dressing. Makes about 1 cup.
Step 1Cover the potatoes with water in a saucepan. Bring them to a simmer and cook until tender, 20 minutes. Drain them, and when cool enough to handle, cut each potato into quarters. Set them aside.
Step 2Blanch the beans in boiling salted water so they remain bright green and crisp, but are slightly tender, 3 minutes. Quickly pop them into a bowl of ice water for a few seconds, then drain them and set them aside.
Step 3Pour enough water in a skillet to cover the fish (but don't add the fish) and add the fennel tops, 1 teaspoon of salt and the pepper. Simmer the water and fennel 10 minutes to flavor the liquid. Add the fish and poach it for 2 minutes, then turn it over and continue cooking until the outside of the fish has turned light beige, 1 to 2 minutes more. Remove the tuna from the skillet and keep it warm.
Step 4Place 1 cup of greens on each of 4 plates. Arrange a portion of the tuna in the center of each bed of lettuce. Divide the vegetables among the plates, surrounding each with the haricots verts, potato quarters, onion, fennel, olives and tomato. Drizzle each salad with about 1/4 cup of the Sauce Gribiche.