Preheat the oven to 200 ° C top / bottom heat. Butter a flat baking dish.
Peel the carrots and cut into oblique slices. Sauté in butter for about 4 - 5 minutes. Season with salt and pepper. Pour in the vegetable stock, cover and finish cooking in about 5 minutes.
Finely chop the parsley, except for something to garnish, and mix with the crème fraîche and mustard. Season with salt and pepper. Salt and pepper the fish.
Put half of the carrots in the baking dish and spread half of the mustard sauce on top. Place the fish fillets on top and spread the rest of the carrots and the remaining cream on top. Bake in the oven on the second rack from the bottom for about 15 minutes. Serve garnished with parsley.