The story could develop with Naruto leaving Konoha to find his own path. He might seek out other ninja villages or hidden places to train and become stronger on his own terms, away from the place and the family ties that he resents.
One possible reason could be the lack of presence of his parents. Growing up without them, he might feel abandoned. And as for Konoha, if he hates it, it could be due to the way he was treated as an outcast, despite being the son of important figures. Maybe the villagers' coldness towards him made him resent the village that didn't seem to protect him from that.
It could also be that Naruto has been influenced by some external force in the fanfiction. For instance, an enemy might have planted false memories or ideas in his head, making him believe that his parents and sister are bad. This false perception could then fuel his hatred.
He could hate them because he felt they were absent during his difficult childhood. Naruto faced a lot of loneliness and bullying, and if he thought his parents could have prevented it but didn't, that would breed hatred.
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.
Emotionally, Naruto would have to deal with a whole new set of family relationships. He grew up without his parents, and now having them back would be a huge adjustment. He might struggle to fit into a 'normal' family dynamic, and there could be some friction as they all get to know each other again.
In some fanfictions, Naruto might find a super - powerful jutsu or artifact. For example, he could discover a long - lost forbidden jutsu that has the power to bring the dead back to life. Or perhaps he stumbles upon a magical item during one of his adventures that is said to be able to revive the deceased.
On a personal level, Naruto would finally get the family he always wanted. But it might also bring some confusion and adjustment issues. His parents would be from a different time, and they'd need to adapt to the new world Naruto lives in. For example, they might be shocked by the new technology and the changes in ninja warfare.
Iruka could play a role. He was Naruto's first teacher who believed in him. He might have some small piece of information that starts Naruto on his journey to find his parents. Then there's Tsunade. As the Hokage, she has access to a lot of secret files. She could either be an obstacle, not wanting Naruto to dig too deep, or she could be a helper, providing him with crucial information. And of course, the Nine - Tailed Fox. It was sealed inside Naruto by his father, so it might have some memories or knowledge related to Naruto's parents that it could share with Naruto.
One possible reason could be some past misdeeds by the parents. Maybe they were neglectful or made decisions that seriously affected Ciel's life in a negative way in the context of the fanfic.