from my experience (AND I MAY BE WRONG) cancun is not much of a fishing town. It is not like other cities (Mazatlan, Cabo) were fishing is one of the top things to do. I know tequilla is more rare in Cancun than other parts of Mexico. You can find fish in the markets as we do back in the states, but again it is not like Puerto Nuevo in Baja California, were they fish out the oysters for you But like i said, I may be wrong. Only the locals can answer better
Puerto Morelos, 20 minutes south of Cancun, is a fishing town like u refer to. Very groovy kind of place too. This link is to the forum of Puerto Morelos that is about the fisherman's co-op. http://www.vivapuertomorelos.com/bb/viewtopic.php?t=144
I've bought fresh fish in Pto Morelos from the fisherman's coop there, and also from the one in Cancun which is near the ferry dock north of Puerto Cancun. But, to be honest, the one in Cancun is quite creepy. Lots of street dogs and garbage all over the beach there and aimless weird people. It's nasty there. It's no place for tourists to go, it's too much of the real Mexico for most tourists to be comfortable. Walmart has about the best seafood of any of the major supermarkets in Cancun imho. Soriana's seafood is not so good, they have the wimpiest, shrimpiest shrimp you ever did see (Soriana has much better produce though).