While I'm a massive fishing nerd in video games, I'm going to address a couple of things.
First, does fishing fit with Geralt? I addressed something similar in this reply
http://forums.cdprojektred.com/threads/30264-Hunger-Thirst-Sleep-amp-Notes?p=1326979#post1326979 mainly Point E but partly also F.
E; Features aren't necessary always a good thing. The sole purpose of this topic is added realism. The problem with this, is that Witcher is a game. It's not catered to be 100% realistic and it shouldn't be, especially if said features interfere with game play. Look at it from this way. Why doesn't CD RED implement a feature where Geralt could cut down trees? He can probably equip an axe and he could then use said axe to cut down trees to gain firewood to his fireplaces and also use it for torches etc (as well as creating forest fires etc). The reason is simple, it doesn't add to what Witcher is as a game (It's not Day Z, it's not Minecraft). It would be treated as a poor mechanics (Just as the stealth system was in Witcher 2 but even more out of context) and would be addressed as one of the annoying features that gamers get annoyed at.
Geralt is a monster hunter, therefore he hunts monster, Geralt is however not a fisherman therefore this mechanic isn't equal compared to hunting. While Geralt isn't a horse racer either it's still a more plausible excuse for CD RED for Geralt to do. He might need money fast then why not. Fishing is mainly though strived for survival (Geralt making a actual living on fishing is a long process and wouldn't make sense with everything going on in the world) and as I stated earlier, this isn't Minecraft or Day Z, therefore Witcher 3 shouldn't pretend to be something it isn't.
Secondly, how do we implement this? It's been addressed time and time again that there won't be any QTE in Witcher 3. Fishing without QTE is rather dodgy though. What will judge whether Geralt gets a fish or not? Fishing games have always relied on having some sort of QTE (at least once you have a fish and intend to reel it in) even if something more simple like how it is in Minecraft were implemented it would mainly feel cheap. Like a rather unwanted mechanic that doesn't fit well with everything else in the game which will (most likely) be extremely polished and thought with massive care.
Thirdly, logic? If the sole purpose is to get food then we need a food mechanic (again I addressed this in the other topic, see above) which deter the gamers from more important features in the game (side-stories, main-story etc) and also takes time away from the developer to develop said features better. On the other hand if it will serve as a alternative "hunting" method then it will simply be a weaker one. You will either be eliminated to get some monsters from few specific areas on the beach (assuming not all monsters are "fish able" which they shouldn't from a game lore perspective) or a sort of combination of beach and the boat which still will be rather dumbfounded on how Geralt will know where each monster are above the surface and watching him sit there trying to dig up the sea Kraken with a fishing rod or a net would just feel off.
Honestly I only see two potential solutions where we won't have a bad mechanic that also doesn't contradict the no QTE policy and the Wither lore "policy"
A, Make some sort of quest related thing where Geralt will fish to find some item, but then again, how will this not feature a QTE event? The closest thing I can think of are something like you get alternatives where and when to fish with what sort of bait and then based on books and your own knowledge can solve this quest. This is however only good once or maybe twice before becoming redundant.
B, Address monster hunting where the sea and water also plays a role. This can be anything from Geralt knowing monster behaviour on certain areas to finding clues/tracks in the beach, on cliffs in the sea etc and use this in concoction with Monster Hunting where Geralt then slays the monster the Witcher way rather than with a net or fishing rod.
Unfortunately this isn't Fable or even Skyrim where fishing can make some sort of sense. Those games are highly flexible with your character where as The Witcher franchise is not, it's focus is the protagonist and the story and we need that those mini-games we get do make sense to the world but are also engaging and exiting for the community, so it doesn't just feel like a cheap attempt from CD RED to prolong the game with useless tat.