Season chicken generously with salt and pepper. Let stand for 30 minutes to 1 hour at room temperature.
Heat over to 400 degrees.
Put an enameled cast iron dutch over over medium heat.
Add the butter and shallots and cook, stirring until softened and lightly browned, about 5 minutes.
Add garlic, chopped tarragon and cook for 1 minute. Don't let garlic brown.
Arrange chicken thighs in the pot in one layer, add the broth and wine, and bring to a simmer.
Put lid on and place dutch over in middle of the oven. Bake for 15 minutes, then lower heat to 350 degrees, and continue baking for 45 minutes, or until thighs are tender.
Put thighs on a platter, cover with tin foil to keep warm.
Strain pan juices through a sieve into a saucepan, and spoon off any rising fat.
Place pan on medium-high heat, add créme fraiche and lemon zest. Simmer until sauce is slightly thickened, about 5 minutes.
Spoon sauce over chicken, garnish with tarragon leaves and serve.