“The name bouillabaisse comes from the method of the preparation — the ingredients are not added all at once. The broth is first boiled (bolh) then the different kinds of fish are added one by one, and each time the broth comes to a boil, the heat is lowered (abaissa).” – wiki
Besides the particular selection of bony Mediterranean coastal fish and Provençal herbs and spices for the stock, Bouillabaisse has some serving rules.
“[…]to me the telling flavor of bouillabaisse comes from two things: the Provençal soup base — garlic, onions, tomatoes, olive oil, fennel, saffron, thyme, bay, and usually a bit of dried orange peel — and, of course, the fish — lean (non-oily), firm-fleshed, soft-fleshed, gelatinous, and shellfish.”
“The fish are served on a platter, and the broth in a tureen, and you eat both together in large soup plates.”
(Julia Child, The French Chef Cookbook., Knopf, 1968)
“Serve the bouillon very hot with the rouille in soup plates with thick slices of country bread rubbed with garlic. Then serve the fish and the potatoes.
(Jean-Louis André, Cuisines des pays de France, Éditions du Chêne, 2001)