Wash fish sections. Clean fennel, put green aside. Boil fish, fennel, lemon and bay leaf in 1 1/4 litre of salted water. Leave to stand for 20 minutes. Skim several times. Peel onions and garlic.
Cut onions into slices. Crush garlic finely. Scald tomatoes, put them briefly in boiling water, rinse with cold water and peel the skin. Halve, seed and quarter the tomatoes. Wash fish and shrimps briefly.
Cut the sea eel and monkfish into two to three centimetre pieces. Clean the mussels, brush them thoroughly under running water. Place in boiling salted water and cook for ten minutes. (Remove closed mussels).
Pour the fish stock through a fine sieve. Heat the oil in a pot. Sauté onions and garlic in it. Add fish stock, thyme, fennel green (put something aside for garnishing) and saffron and bring everything to the boil.
Add the fish, shrimps and tomatoes to the stock and simmer at low heat for 10 to 15 minutes. Season soup with salt and pepper, add mussels and add some fresh fennel green.
Serve with aioli (garlic mayonnaise) and fresh baguette.