The problem with the law was that it was in reality imposing a time of starvation every year to the fishermans and their families, while the same species could be bought at the markets imported from other countries. The measure was one of the first to be abandoned when the political regime changed.
I don't really know what is the possibility of fishing companies to cycle between the fishing species during the year to let the other species grow, but that still seems like an alternative to me.
I also think that a fish diet is much more healthy than a meat diet, so a danger like the possible extinction of fishing species shouldn't be taken lightly just because we can get the proteins somewhere else.