Preheat oven to 450°.
To prepare panzanella, place bread in a single layer on a baking sheet. Bake at 450° for 4 minutes or until toasted.
Heat a nonstick skillet coated with cooking spray over medium-high heat; add peach, nectarine, and 1 tablespoon sugar. Cook 2 minutes or until chopped fruit is lightly browned, stirring the mixture frequently.
Combine the fruit mixture, tomato, olives, basil, onion, and capers in a large bowl. Combine 2 tablespoons sugar with olive oil, vinegar, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a small bowl, stirring with a whisk. Add vinegar mixture to peach mixture; toss gently to combine. Let stand 30 minutes. Toss with bread just before serving.
To prepare chicken, combine shallots and next 5 ingredients (shallots through 1/8 teaspoon black pepper) in a large zip-top plastic bag; add chicken. Seal and marinate in refrigerator 30 minutes. Remove chicken from bag; discard marinade. Sauté chicken in a large nonstick skillet over medium-high heat. Slice chicken; serve with panzanella. Garnish with thyme sprigs, if desired.