In many such fanfictions, Naruto and Hinata might be sent back in time through some magical or jutsu - related means. Once they meet their parents, it could be a very emotional moment. Naruto might see his father Minato and mother Kushina, and Hinata could meet her father Hiashi. They could learn a lot about their families' pasts and perhaps even change some things for the better in the timeline.
One possible scenario in such a fanfiction could be that Naruto's parents are preoccupied with their shinobi duties. They might be constantly on missions for the Hidden Leaf Village, leaving Naruto at home with caretakers who don't really pay him much attention. This could lead to Naruto feeling lonely and isolated, just as he did in the original story when he thought he had no family.
The story would be very different. Naruto's parents being alive would mean he has a support system from the start. His father could pass on his jutsu and wisdom more directly. Naruto might not have the same drive to become Hokage in the same way, as he wouldn't be seeking that family - like recognition from the village. His mother's presence would also add an element of warmth and stability to his life. And perhaps he would be more of a prodigy with both his parents' guidance, changing the power dynamics in the ninja world.
One common plot point is that Naruto uses his future knowledge to protect his parents. For example, he might know about an upcoming attack on the village and warn his father, Minato. Another is that he gets to experience a normal family life, which he never had in his original timeline. This often leads to a change in his personality, as he becomes more confident and less of an outcast. Also, Naruto usually tries to change the future for the better, like preventing the deaths of some of his friends or making the village stronger against future threats.
The exploration of Naruto's powers is crucial. Since he's godlike, his powers are likely to be extraordinary. His parents, being experienced ninjas, can help him understand and manage these powers. Also, the fanfiction might focus on how the ninja world reacts to a godlike Naruto with his parents alive. Some might fear him, while others might see him as a savior. This creates a complex web of relationships and storylines.
A fanfiction might depict fem Naruto's life with her parents alive as a story full of family moments. They could celebrate birthdays and festivals together. Minato and Kushina would be able to guide fem Naruto in her social life too. She wouldn't be the lonely outcast she was in the original story. Instead, she would be a popular kunoichi with her parents' reputation. Her parents could also help her develop her own fighting style that combines their techniques, making her a very strong and unique ninja in the Hidden Leaf Village.
One possible storyline could be that Naruto's parents, Minato and Kushina, are alive and they train Naruto from a young age. This would make Naruto an even more powerful ninja earlier on. He would grow up with their love and support, and perhaps not be as much of an outcast in the village as he was in the original story.
In a fanfiction where Naruto's parents are alive, they could play a major role in changing the politics of the Hidden Leaf. Minato, being a former Hokage, and Kushina with her strong Uzumaki blood, might work together to strengthen the village's defenses and relations with other villages. This would also mean Naruto doesn't have to struggle alone and could learn advanced techniques much earlier from his parents.
I really liked 'Back to the Beginning with Naruto'. Here, when Naruto travels back in time, his parents are alive. The story focuses on how Naruto tries to prevent the tragedies that happened in the original timeline. It's interesting to see how his knowledge from the future impacts the past. For example, he is able to warn his father about certain threats, and it changes the course of events. And the relationship between Naruto and his parents is beautifully portrayed, full of love and understanding.
He would be more confident. Growing up with his parents' love and presence would mean he doesn't have to constantly seek validation. So he might be less brash and more self - assured from the start.