Preheat the oven to 220C/425F/Gas 7.
Bring a pan of water to the boil. Place the carrots into the pan and cook for 5-10 minutes, or until tender. Drain the carrots, add butter and tarragon and stir.
For the chicken, season your chicken with salt and freshly ground pepper. Heat the butter and oil in an ovenproof pan and fry the chicken skin-side down for three minutes, then turn the chicken over and transfer to the oven to roast for 10 minutes, or until completely cooked through.
To make the sauce, bring the wine and shallot up to the boil in a clean saucepan, then simmer until reduced by half for five minutes.
Add the cream to the sauce and simmer to thicken. Gently stir the sauce, adding the tarragon, and season, to taste, with salt and freshly ground black pepper.
Crumble the Reblochon cheese onto the sauce and stir though until melted.
To serve, place the carrots onto a plate. Place the chicken on top, drizzle over the sauce and garnish with a sprig of tarragon.