Using a large skillet, simmer tuna fillets, tarragon, salt, and pepper covered over medium-high heat in 1 inch of water for 8 minutes. Remove tuna to a plate, reserving liquid in skillet, and chill for at least 1 hour before serving.
Bring the water in skillet to a boil and add potatoes and green beans cover with a lid. After 4 minutes, remove the green beans with a slotted spoon and rinse immediately in cold water; set aside. Allow the potatoes to cook for an additional 6 minutes. Remove potatoes from hot water and allow to cool on a plate; slice when room temperature
Place 4 lettuce leaves on each chilled plate. Evenly dividing ingredients, arrange tuna fillets, potatoes, green beans, tomatoes, eggs, olives, and capers on the beds of lettuce. Drizzle with vinaigrette and serve.
Lemon Mustard Vinaigrette
Put all ingredients in a glass jar, seal with a lid, and shake until ingredients are well incorporated. Refrigerate leftovers