Place the chicken in a large, deep, non-reactive casserole dish. Layer the carrots, onion, celery, tomato, garlic, thyme, bay leaf, parsley, and pepper evenly over the chicken pieces. In a small bowl, mix together the red wine, Cognac, and oil. Drizzle the wine mixture over the vegetables and chicken, and then marinate the mixture overnight, for 8-12 hours.
Preheat the oven to 425F. Melt 3 tablespoons of butter in a large skillet over medium-high heat. Remove each piece of the chicken from the marinade, reserving the liquid, and brown them on each side. Set aside the chicken, scoop the vegetables out of the marinade, and cook them in the skillet for 5 minutes, until they begin to get tender.
Arrange the chicken in a deep, glass casserole dish, layer the vegetables over the chicken, and pour the reserved liquid over the casserole. Sprinkle the salt and sugar over the mixture, cover, and bake it in the preheated oven for 20 minutes.
While the chicken is baking, fry the bacon in the skillet until it is crispy and set it aside to drain. Pour off all but approximately 2 tablespoons of the bacon grease and sauté the mushrooms and onions over low-medium heat for 6-8 minutes, until they turn tender. When the chicken has cooked for 20 minutes, remove it from the oven and add the bacon, mushrooms, and onions. Cover and return the casserole to the oven for 20 minutes.
Mix together the 2 tablespoons softened butter and the all-purpose flour until they form a smooth paste. Add the butter-flour mixture, or beurre manie, to the chicken and vegetables for the last 5 minutes of cooking. Remove the casserole from the oven and stir the beurre manie throughout the dish. Now add the Foie Gras to the chicken, cover and turn oven off and place in oven for 5 minutes. Remove from oven, allow it to sit and thicken for a few minutes before serving. Serve with good crusty bread. The Foie Gras will take this over the top with decadence but in moderation is great.