Mix the olive oil, garlic, saffron, lemon zest, salt, pepper, fennel seeds, herbes de Provence, onion, celery and carrot in a large bowl. Slice chicken into bite size chunks. Add the chicken and turn to coat. Cover and refrigerate until you are ready to cook.
Transfer the contents of the bowl to a large saucepan. Add the tomatoes, wine, water and potatoes. Cover and bring to a boil over high heat. Reduce the heat to low and simmer gently for 25 minutes. Add the sausage and cook for 5 minutes longer.
Transfer 2 of the cooked potato quarters and 0.25 cup of liquid from the saucepan to a food processor. Add the garlic, cayenne and paprika; process for 10 seconds. Add the egg yolk. With the processor on, pour in the olive oil, and process for a few seconds, until incorporated. Season with the salt.
Serve the bouillabaisse in warm soup plates with a spoonful of the rouille drizzled on top.