They DID go fishing. As much as they were able to. 'Fishing' is a logical step in times of famine, and there is absolutely no reason they would not have tried it, to the best of their resources.
Several factors would have stood in their way, however. First of all, fishing from the shore is not highly productive. Second, most farmers would have lived a long distance from the sea, or from convenient lakes and rivers--Many of which were state-owned or owned by landlords, which made them inaccesible. This left, as the only possibility, learning how to get out on a ship and go fishing; which is not easy to do. (If you've never gone fishing before, ask anyone who's done so.) It's something that requires a fair amount of skill. And then, they would be in competition for fish with all the other highly-skilled fishermen.
Finally, it must be noted that 'food security' is something that belongs to modern times. Until the 19th century (or possibly later) famine was a regular event in Europe, occurring every 5-10 years.
(Which is one reason why, if you walk into a historic graveyard, you'll find many deaths of people who are very young.) Europe was not able to cure previous famines with fishing; nor could it by this means cure the Potato famine.