Preheat oven to 400 degrees.
Remove giblets. Place the chicken breast-side down on a cutting board. Use heavy-duty kitchen scissors to cut out the backbone by cutting down from neck to tail along each side. Remove and discard. Open the bird up like a book. Use a sharp paring knife to cut down the center of the bird, just deep enough to incise the cartilage covering the breastbone. Turn the chicken over and press down on the chicken to flatten it completely.
Pat the chicken dry with paper towels, season with salt, pepper, and place it in the roasting pan.
Brush the dijon mustard evenly over the chicken, sprinkle the tarragon over evenly. Then spoon the creme fraiche over the chicken.
Roast for 40-60 minutes, until the thickest part of the breast registers 150°F on an instant-read thermometer and the legs are at least 175°F.
Remove the chicken from the pan to a cutting board or plate to rest.
Remove all but 2 tablespoons of fat from the roasting pan. Place the pan over medium-high heat and bring to a boil, whisk in 1 tablespoon of flour and cook for at least 1 minute. Add the 1/4 cup of white wine, 1 cup of chicken stock, and boil until it thickens about 3-4 minutes.
Slice the chicken into serving size pieces and drizzle with the sauce.