Place potatoes in a medium saucepan. Cover with water; bring to a boil. Reduce heat; simmer 7 minutes. Add beans; cook an additional 3 minutes or until beans are crisp-tender. Drain.
Heat 1 tablespoon oil in saucepan over medium heat. Add shallots; saute 3 minutes. Add potatoes, beans, and garlic; cook 3 minutes, stirring occasionally.
Cook pasta according to package directions, omitting salt and fat. Drain; set aside.
Combine 2 tablespoons oil, tarragon, mustard, vinegar, and salt; stir well. Combine pasta, potato mixture, and tuna in a large bowl; toss well. Drizzle mustard mixture over pasta mixture, tossing gently to coat. Serve with freshly ground pepper.