He would be extremely confused. Harry has always thought of his parents as heroes, and suddenly finding out they betrayed him would shatter his world view. He'd question everything he believed in.
In some fanfiction, the idea of Harry Potter being betrayed by his parents might be justified through a complex web of magic and prophecy. Maybe the parents thought sacrificing Harry was the only way to save the wizarding world from a greater evil. However, this goes against the essence of their characters in the original books.
In such a fanfiction, perhaps the parents were forced to betray Harry due to some dark magic or a powerful enemy threatening them. Maybe they had to give up Harry to save the wizarding world from an even greater evil.
Perhaps his parents were part of a secret and evil organization all along. They pretended to be good but in fact were planning something big and Harry was just a pawn in their plan. So they betrayed him by leaving him exposed to danger or even trying to harm him directly. In the fanfiction, Harry could then go on a journey to discover the truth about his parents and their real motives.
If Harry was betrayed by his parents in fanfiction, he would likely become a much more cynical and distrustful person. His whole world view was based on his parents being heroes, so this betrayal would shatter his beliefs and make him question everything.
Yes, there might be some extremely dark and out - of - canon fanfictions out there with such a disturbing premise, but it goes against the general nature of the original story where Harry's parents loved him deeply. However, in the vast world of fanfiction, people can create all kinds of strange and often inappropriate scenarios.
If Harry's parents are the ones who betrayed him, they could be considered the main antagonists in a sense. They created this false image of themselves as loving parents when in fact they had ulterior motives. Another possibility could be a character who was in on the parents' plan and now is trying to cover it up or continue the malicious work they started. Maybe it's an old acquaintance of his parents from their days at Hogwarts who is now out to stop Harry from finding out the truth.
Well, perhaps in the fanfiction, it shows that Harry's parents made a deal with Voldemort before their deaths. They promised to hand Harry over in exchange for something, like power or protection for themselves. But then things went wrong and they ended up dying, still leaving Harry feeling betrayed as he discovers this truth later. It could also be that his parents were actually working against the Order of the Phoenix all along and Harry was just a pawn in their real plan.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.