1 cup tarragon sprigs or 1 teaspoon dried, crumbled
3 fresh parsley sprigs
3 large thyme sprigs or 1/2 teaspoon dried, crumbled
1 bay leaf
1 teaspoon pepper
1/4 cup creme fraiche or whipping cream
Season chicken with salt and pepper. Melt butter in heavy large deep skillet over medium-high heat. Add chicken and brown on all sides, turning occasionally, about 5 minutes. Transfer chicken to plate. Add onion, carrot and garlic to same skillet and saute until onion is just translucent, about three minutes. Mix in tomato paste, then tomatoes, vinegar, wine, 4 tarragon sprigs or 1 tsp. dried tarragon, parsley, thyme, bay leaf, and pepper. Bring mixture to simmer. Return chicken pieces to skillet. Reduce heat to medium and simmer until chicken breasts are cooked through, turning chicken once, about 25 minutes. Transfer breasts to platter. Cook leg pieces until cooked through, about 5 minutes longer, and transfer to platter.
Pour contents of skillet through sieve, pressing hard on solids with back of spoon. Return sauce to skillet and boil until reduced to 1 cup, about 15 minutes. Whisk in creme fraiche. season sauce to taste with salt and pepper. Return chicken to skillet and simmer just until heated through, about two minutes.
Arrange chicken on platter. Spoon sauce over. Garnish with remaining tarragon sprigs and serve.