Heat a large nonstick skillet coated with cooking spray over medium-high heat. Drizzle fish with 2 teaspoons oil, and sprinkle with 1/4 teaspoon salt. Add fish to pan; cook 4 minutes on each side or until fish flakes easily when tested with a fork.
While fish cooks, combine 1 teaspoon oil, 1/4 teaspoon salt, tarragon, and the next 5 ingredients (tarragon through peppercorns), stirring with a whisk. Drizzle 1/4 cup vinaigrette over greens; toss gently to combine. Arrange about 1 1/4 cups greens on each of 4 plates. Top each serving with 1 fillet; drizzle each serving with 1 tablespoon vinaigrette.