Coconut milk is made from shredded coconut that is simmered in water and then strained to make a creamy liquid. It should not be confused with coconut cream, which has less water, or with sweetened cream of coconut. Reduced-fat coconut milk contains thickeners and other additives; it's best to use small amounts of regular coconut milk instead.
Classic bouillabaisse calls for fish native to the Mediterranean, many of which -- John Dory, weever, and rascasse -- are hard to come by in the United States. However, many fish in American waters are suitable. Avoid oily fish when making your selection. Halibut, red snapper, and monkfish are particularly good choices. The addition of mussels and lobster is not traditional but very delicious. In the French manner, bouillabaisse is served in two courses: the soup first and then the fish. It is just as good when fish and soup are served together.