In an 8-quart or larger pot, heat the olive oil over medium heat. Add the onion, leek, fennel, and garlic and cook, stirring, until soft, about 6 minutes. Add the tomatoes and cook, stirring, for 1 minute. Stir in the Pernod, wine, and saffron, increase the heat to medium-high, and cook for 1 minute more. Add the potatoes, salt, and pepper and stir well, then add the stock and bring to a boil. Add the bay leaf, thyme, parsley, and peppercorns, lower the heat, and simmer until the potatoes are just tender but still firm, 20 minutes. Add the clams, mussels, and fish, cover the pot, and cook for another 10 minutes, or until the clams and mussels have opened and the fish is just cooked through. Remove from the heat and discard any unopened clams or mussels.

Ladle about 1 cup of the hot broth into a heatproof bowl and briskly whisk in 3 tablespoons of the aïoli to form an emulsion. Pour the emulsified broth-aïoli mixture back into the bouillabaisse and stir to combine.

To serve, ladle the soup into large soup bowls and garnish with chopped parsley. Serve with warm baguettes and the remaining aïoli.