Combine rosemary, lemon zest, 1/2 teaspoon salt, 1/2 teaspoon pepper, and garlic in a small bowl. Place chicken, breast side down, on a cutting board. Using kitchen shears, cut along both sides of backbone; discard backbone. Turn chicken breast side up; press firmly against breastbone with the heel of your hand so that the bird is splayed open, butterfly style. Trim excess fat; tuck wing tips under chicken. Place chicken in the middle of a 13 x 18–inch half sheet pan coated with cooking spray. Starting at neck cavity, gently loosen skin from breasts, drumsticks, and thighs by inserting fingers, gently pushing between skin and meat. Rub herb mixture under loosened skin over breasts, drumsticks, and thighs.
Starting at the outermost edges, cut most (but not all) of the way through each potato at 1/8-inch intervals. Arrange potatoes around chicken on pan; brush potatoes with 1 tablespoon oil. Bake potatoes and chicken at 450°F for 45 minutes or until a thermometer inserted in meaty part of chicken thigh registers 165°.
Meanwhile, cut zucchini into noodles using the large holes of a spiralizer. Pat dry with paper towels. Cut zucchini noodles into manageable lengths (no longer than 4 or 5 inches). Combine cornmeal, cornstarch, garlic powder, and paprika in a large bowl. Add zucchini noodles; toss well to coat.
Remove pan from oven; place chicken on a cutting board (leave potatoes on pan). Wipe excess chicken juices from center of pan with paper towels. Recoat pan with cooking spray. Brush remaining 1 tablespoon oil over potatoes. Arrange zucchini noodles on pan, shaking off any excess cornmeal mixture; spread zucchini as evenly as possible into a single layer (see note above). Bake at 450°F for 15 minutes or until zucchini is crisp-tender and potatoes are done. Sprinkle potatoes and zucchini with remaining ¾ teaspoon salt and ½ teaspoon pepper. Discard skin from chicken; serve chicken with potatoes and zucchini. Serve immediately.