1. Coat the chicken with the mustard and set it in a bowl, covered, to marinate at room temperature for 2 hours.
2. Preheat the oven to 350° F
3. Arrange the chicken, skin side up, in a flameproof baking dish. Scrape out any mustard remaining in the bowl and spread it evenly over the chicken. Season lightly with pepper and pour the vermouth or wine around the chicken.
4. Set the dish on the center rack of the oven and bake, basting occasionally, until the chicken is done, 1 hour. You may have to bake the dark meat sections for another 5 to 10 minutes.
5. Scrape the mustard off the chicken and back into the baking dish. Transfer the chicken pieces to a serving platter, cover, and keep warm.
6. Skim as much fat as possible from the cooking juices and set the baking dish over medium heat. Bring to a boil, whisk in the crème fraiche or heavy cream, and lower the heat. Simmer the sauce until it is reduced by about one third, 5 to 10 minutes. Season lightly with salt and pepper. Teaste, correct the seasoning, and spoon the sauce over the chicken. Serve hot or at room temperature.