Roll the rabbit pieces in the flour to coat them well. Peel and wash the carrots, then cut into thin slices. Peel and chop the onion. Preheat the oven to 400°F. In a casserole dish that can go in the oven, heat the oil over medium heat. Brown the rabbit pieces for 2 minutes on each side and set aside. Put the carrots and onion in the casserole dish.
Cook for 1 minute over low heat, then add the rabbit back in with the white wine and bouquet garni. Season with salt and pepper, and mix. Bring to a boil, cover, and put in the oven for 40 minutes. Cook the mushrooms for 10 to 15 minutes in a pan, in hot butter, over medium heat. Season with salt and pepper. Arrange the rabbit pieces, with a slotted spoon, in a hot serving dish. Pour the cream and mustard into the casserole dish. Bring to a simmer, stirring, then remove from the heat and strain over the pan with the mushrooms, using a fine mesh sieve. Mix and adjust the seasoning. Pour the sauce over the rabbit and serve.