Cut each poussin into 6 serving pieces, and season with salt and pepper. Place in a bowl, add shallots and thyme, and mix well. Add wine, cover, and marinate in refrigerator for 12 hours.
Preheat oven to 350 degrees. Remove pieces of poussin from marinade, and pat dry. Reserve marinade. In a large skillet, heat olive oil over medium-high heat. Add as many poussin pieces as will fit without crowding in one layer, skin side down, and sear until golden brown; remove from pan. Repeat with remaining poussin pieces.
Divide poussin pieces among 6 3-cup ovenproof casseroles. (Dish may also be prepared in a large Dutch oven.) Deglaze skillet with a little chicken broth, and add liquid to casseroles along with vegetables, tarragon, bacon, reserved marinade, and remaining chicken broth. Cover and bake for about 45 minutes.