Clean the mussels and wash them thoroughly. Discard opened mussels. Peel and slice the shallots. Peel and slice the garlic. Peel and wash the carrots.
Clean fennel, wash it. Cut carrots and fennel into slices. Peel and wash celery and cut it into leaves (2x2 cm). Heat oil in a pot, fry shallots, garlic, carrots, celery and fennel in it until transparent.
Season with salt and pepper. Pour on white wine and 1/2 litre water and bring to the boil. Add mussels and cook in a closed pot at moderate heat for about 8 minutes. In the meantime wash parsley, shake dry, pluck leaves from the stalks and cut into strips.
Pour the mussels onto a sieve and collect the stock. Discard unopened mussels. Measure out 500 ml of mussel stock and mix with crème fraîche and add back to the mussels. Sprinkle with parsley.