Preheat oven to 375˚F. Take out the chicken about 15 minutes before cooking, wash, clean and pat dry.
With a spoon, mash the thyme and butter together until well combined.
Use a knife to gently loosen the chicken’s skin. Stuff the mixed thyme and butter evenly underneath the skin.
Combine 3 tbsp of olive oil, salt, and pepper in a mixing bowl. Use your fingers to massage the entire chicken with the mixture.
Fill the cavity with the orange and thyme sprigs. Truss the chicken securely with kitchen twine.
Place the chicken, breast side down in a baking dish and roast for 15 minutes.
Mix creme fraiche with garlic, shallot, and thyme.
Toss the potatoes and carrots with olive oil and a pinch of salt and pepper.
Remove the chicken from the oven and carefully turn the chicken breast-side up. Rube the creme fraiche all over the top of the chicken.
Scatter the potatoes and carrots in a single layer around and underneath the chicken.
Transfer the baking dish to the oven and cook for 1 hour. Baste the chicken and vegetable with pan juices. If the chicken starts to brown, place a large piece of aluminum foil over the breast to prevent it from burning.
Roast the chicken for another hour or until an instant-read thermometer inserted in the thickest part of the chicken thigh reads 175˚F and the vegetables are tender.
Remove the chicken from the oven and let it rest for 15 minutes before serving.