Whisk lemon juice, mustard, shallot, 1 teaspoon tarragon, ½ teaspoon salt, and ¼ teaspoon pepper together in large bowl.
Whisking constantly, slowly drizzle in oil. Add arugula, apples, and fennel and gently toss to coat. Season with salt and pepper to taste.
Divide salad among plates and top with flaked trout. Sprinkle with remaining tarragon. Serve immediately.
