Divide thyme and sage each into 4 equal portions. Loosen skin from chicken over breasts and thighs; insert thyme under skin over each breast and thigh.
Over medium-high flame, heat a 12-inch cast-iron skillet. Season chicken with salt and pepper. Place chicken skin side down in skillet with leg portion closest to the handle. Cook until skin is lightly browned, about 4 minutes. Turn chicken over; place sage on each breast and thigh. Remove 10-inch skillet from oven; place on top of chicken (bottom down) so handles match.
Pan-roast chicken 30 minutes. Remove top skillet. Cook chicken 10 more minutes. It is done when meat thermometer inserted in thickest part of thigh (without touching the bone) reads 175° to 180° and juices run clear when pierced with a sharp knife. Let chicken stand 10 minutes before carving. To make the fries, preheat oven to 400°F with a 12-inch cast-iron skillet inside. In a large bowl, toss potatoes, 2 teaspoon oil, 1/4 teaspoon salt, and pepper.
Brush hot skillet with remaining 1 teaspoon oil. Place potatoes in skillet. Oven-roast them until browned on bottom, about 20 minutes. Turn them over and sprinkle with onion. Lightly coat rosemary and sage sprigs with cooking spray; add to potatoes. Oven-roast potatoes until browned and tender, 15 to 20 minutes. Sprinkle with remaining 1/4 teaspoon salt. Stack potatoes with herbs on a warm platter.