In a large bowl, combine 2 tablespoons olive oil, minced garlic, chopped rosemary, lemon zest, smoked paprika, onion powder, 3/4 tsp salt, and 1/4 tsp black pepper. Stir into a thick paste and let sit 5 minutes for flavors to meld.
Pat chicken thighs completely dry with paper towels, then loosen the skin and press rosemary rub directly under the skin and all over the outside. For best results, refrigerate uncovered up to 24 hours — even 30 minutes at room temperature makes a noticeable difference.
Preheat oven to 425°F (220°C). Line a large rimmed baking sheet with foil if desired, place a wire rack on one half of the pan for the chicken, leaving the other half for the fries.
Peel and cut potatoes into 1/4-inch sticks, soak in cold water for at least 10 minutes, then drain and pat completely dry. Toss with 1 tablespoon olive oil, garlic powder, 1/4 tsp salt, and 1/4 tsp pepper until evenly coated.
Place chicken skin-side up on the wire rack and spread fries in a single layer with no overlapping on the open side of the pan. Roast for 25 minutes, then flip the fries and continue roasting for 15 to 20 more minutes.
In the last 5 minutes, brush chicken skins with melted butter. Chicken is done when skin is deeply golden and internal temperature reads 165°F (74°C); fries should be golden and crisp. Broil for 2 to 3 minutes if skin needs more color.
Rest chicken on the rack for 5 minutes before serving. Immediately season hot fries with flaky sea salt, garnish with fresh rosemary sprigs, and serve together on a platter.