Steam potatoes, covered, 15 minutes or until tender; cool slightly. Combine potatoes and wine in a bowl; stir gently to coat. Steam green beans, covered, 6 minutes or until crisp-tender. Rinse under cold water; drain.
Combine 2 tablespoons shallots, 1 tablespoon Dijon mustard, and tarragon in a bowl. Add chicken, tossing well to coat. Place chicken on a broiler pan coated with cooking spray, and broil for 6 minutes on each side or until chicken is done. Cool slightly; slice into 1/2-inch strips.
Combine 2 tablespoons shallots, 1 tablespoon Dijon mustard, vinegar, oil, anchovy paste, and garlic in large bowl. Add potatoes and green beans; toss gently.
Spoon 1 1/4 cups potato mixture onto each of 4 plates; top each portion with one-fourth of chicken strips. Arrange the tomatoes on each salad, and sprinkle with green onions.