In a 10- by 15-inch baking pan, mix walnuts with 1 tablespoon oil, the sugar, and 1/2 teaspoon salt; spread level. Bake in a 350° oven, stirring occasionally, until nuts are golden brown, about 15 minutes. Let cool.
In a large bowl, mix vinegar, shallots, mustard, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Slowly whisk in 1/3 cup oil until vinaigrette is emulsified. Add lettuce, grapes, red onion, tarragon, and sugared walnuts; mix gently to coat, adding more salt and pepper to taste.