Arrange chicken on rimmed baking sheet and sprinkle each side of each piece with 1/4 teaspoon salt. Cover with plastic wrap and chill overnight. Preheat oven to 350°F. Heat 1 tablespoon oil in large nonstick skillet over medium-high heat. Transfer chicken to skillet and sear until golden, 5 to 6 minutes per side. Transfer chicken to heavy roasting pan, skin side up. Add carrots, shallots, garlic, 1 teaspoon thyme, lemon peel, ras-el-hanout, chicken broth, white wine, and remaining 3 tablespoons olive oil to skillet. Bring to boil, whisking up brown bits. Pour mixture over chicken in roasting pan and bring to simmer over medium heat. Cover with foil; place in oven. Braise 1 hour, until tender. Transfer chicken, carrots, and shallots to baking sheet; discard garlic. Pour pan juices into large saucepan. Spoon off fat from surface. Boil juices until reduced to 1 3/4 cups, whisking occasionally, about 18 minutes. Add figs and vinegar; cook until figs are just heated through, 3 to 4 minutes. Season with salt and pepper. Place cooked couscous on large plate. Top with chicken, vegetables, and figs. Spoon sauce over chicken and figs. Garnish with fresh herbs and serve immediately.