Preheat the oven to low. Trim any excess fat from the chicken and pat dry with paper towels. Dust with the flour and season lightly with salt and pepper.
Heat the butter and 1 tablespoon oil in a frying pan over moderate heat and cook the chicken for about 6 minutes on each side.
Meanwhile, peel and chop the shallots. Snip off the tip of each sprig of tarragon and reserve, then strip the leaves from the remaining stems, chop coarsely and put aside.
Transfer the chicken to the oven to keep warm. Add the shallots to the pan with the rest of the oil and fry, stirring, for 1 minute. Add the wine and half the chopped tarragon. Boil until the wine has reduced by half. Add the chicken stock and reduce by half again.
Stir in the crème fraîche and the remaining chopped tarragon, then return the chicken to the pan and warm through for 1 minute on each side. Adjust the seasoning and serve, garnished with tarragon tips.