Cut duck into serving pieces and place in a porcelain or earthenware bowl. Add salt and freshly ground black pepper, celery, carrots, sliced onions, cognac and red wine; marinate the duck in this mixture for at least 2 hours.
Remove duck pieces from the marinade; drain and dry with a clean cloth. Sauté diced bacon in olive oil until golden. Remove bacon bits, and brown duck pieces in fat. Place bacon bits and duck pieces with pan juices in a large heatproof casserole, cover, and simmer gently for 20 minutes.
Add the marinade, bouquet garni, garlic and mushrooms. Simmer over a very low heat for 1½ hours, or until duck is tender. Remove bouquet garni’, skim fat, correct seasoning and serve from the casserole.