Preheat oven to 425°F with rack in middle.
Pull off excess fat around cavities of chicken and discard, then rinse chicken and pat dry. Mix together 1 1/2 teaspoons salt and 1 teaspoon pepper and rub inside cavity. Chop enough tarragon to measure 1 1/2 tablespoons and set aside, then add remainder of bunch to cavity.
Put chicken in a flameproof shallow roasting pan or gratin dish and rub all over with 1/3 cup mustard. Tie legs together with string and roast until an instant-read thermometer inserted into fleshy part of a thigh (do not touch bone) registers 170°F, 45 minutes to 1 hour.
Carefully tilt chicken so juices from cavity run into roasting pan, then transfer chicken to a cutting board and let stand 10 minutes.
Pour off all but 2 tablespoons fat from pan. Whisk in flour, then cook over medium heat, whisking, 1 minute. Add water, whisking constantly and scraping up brown bits, and bring to a boil. Simmer sauce until slightly thickened, then whisk in cream, remaining tablespoon mustard, and salt and pepper to taste.
Strain sauce through a fine-mesh sieve into a bowl, discarding solids, then stir in reserved chopped tarragon. Serve chicken with sauce.
