He might be angry at first. Naruto has grown up alone and had to fight for acceptance. So when his parents say they regret abandoning him, he could lash out, saying it's too late. After all, he has already faced so much without them.
In some fanfictions, Naruto may become extremely bitter. He could feel a deep sense of betrayal and this might fuel his determination to become stronger, not for the sake of the village at first, but more for self - vindication. He might isolate himself from others and struggle with his identity.
Naruto would probably be overjoyed at first. After all, he has always longed for his parents. But with the sister, it might be a bit more complicated. He might be a bit cautious, not sure how to interact with her at first. But eventually, he would welcome her into his life with open arms.
Well, a common reason in fanfic could be that his parents are on a top - secret mission. This mission is so crucial and dangerous that they can't take Naruto with them. They have to sacrifice being with their son to fulfill their duties for the greater good of the ninja world.
In some fanfictions, his parents might be forced to abandon him due to a powerful enemy threatening their family. They may believe that by leaving Naruto alone, the enemy will not target him immediately, thinking he's just an ordinary orphan.
At first, Naruto would likely be very confused and hurt. He has always craved family love and acceptance, so this sudden turn would be a huge blow. He might try to plead with his family, asking them to believe him and give him a chance to explain.
One possible reason could be that Naruto has some sort of power within him that they fear. Maybe it's a power that they don't understand and think could be dangerous, so they hate him out of fear.
In this fanfiction, it could be that Naruto's parents were under some sort of mind - control. Some evil entity could have taken over their minds and made them feel hatred towards Naruto. Also, it might be related to a family secret or feud. There could be something in the family's past that made them believe Naruto was a stain on their family name, even though Naruto himself was innocent. It could also be a case of false information being spread around the village which made his parents believe lies about him.
One possible reason could be a curse. Maybe some enemy put a curse on Naruto's parents that made them forget about him. It could be a way to get back at them by targeting their most precious thing, which is their son.
Minato and Kushina would likely have a complex reaction. They would be proud of Naruto's heroic deeds in fanfiction. But if they saw him being in danger or having a hard time, they would be worried. Also, if there are parts where Naruto's values seem different from what they taught him, they might be a bit confused.