In such a fanfiction, Naruto would likely grow up with a strong sense of family. He'd be trained by his father, Minato, from an early age, perhaps becoming a prodigy even faster. His mother, Kushina, would fill his life with love and warmth, and he might not have the same underdog status as in the original. He could be more confident and less of a prankster, having a stable home environment.
The plot could start with Naruto growing up in a happy family. He'd learn about the village and ninja ways in a more positive environment. His first missions might be more successful as he has his parents' advice. As he grows, he might face threats to the village earlier, but with his family by his side, he'd be better equipped to handle them.
One possible storyline could be that Naruto grows up with his parents' love and training. He might become an even more powerful ninja at a younger age. Since Minato was a prodigy and Kushina had strong chakra, they could pass on their skills and knowledge early. Naruto could also have a different personality, more confident and less of an outcast as he has a loving family from the start.
Naruto's social skills would also be different. Instead of being the lonely outcast, he would be part of a family. He would interact with other ninja kids in a more positive way. His parents could also guide him in making friends. He might be more diplomatic in his relationships because he has seen how his father, as the Hokage, dealt with people. This would all contribute to a very different Naruto compared to the one we know from the original series.
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.
One possible plot could be that Harry grows up in a loving and magical home. He gets to learn magic from his parents at a very early age. His father, James, might teach him Quidditch skills right in their backyard. His mother, Lily, could pass on her knowledge of potions and herbology. They would also protect him from the dark forces that are still out there, perhaps leading to some epic battles where the family stands united against the remnants of Voldemort's followers.
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.
Naruto's departure from his parents may initially cause him to be more reckless as he tries to prove himself without their guidance. However, over time, he could learn to be more cautious and calculated. This change in behavior would be a significant part of his character development, as he transitions from a somewhat naive boy to a more mature and self - reliant ninja.