One possibility is that Naruto would finally experience the love and guidance of his parents that he always longed for. Minato could train him from a young age, passing on his powerful jutsu. Kushina would be there to comfort him when he's sad. They could all have family dinners together, and Naruto would grow up in a warm and loving environment, which would likely make him a more confident and less lonely child.
Naruto would be more self - assured. Growing up with his parents' love and support, he wouldn't have to constantly seek attention in a desperate way. He'd know his worth from the start.
It could be that in a special mission, Naruto discovers a hidden jutsu that allows him to communicate with the spirits of his deceased parents, leading to a touching reunion.
Perhaps Naruto has always felt different from others in the village. And when he finally learns about his parents, he realizes that their actions, even if they were for a good cause like protecting the village, still made his life very difficult. He might be angry that they didn't find a better way to handle things so that he didn't have to suffer so much growing up.
His relationship with his parents would be loving. Minato would be a strict but fair father, teaching Naruto about ninjutsu and the responsibilities of being a shinobi. Kushina would be the warm, affectionate mother, always there to comfort and encourage Naruto. They would support his dreams and be proud of his every achievement.
It might make him more distant from his friends at first. He could be so consumed by his anger towards his parents that he withdraws from his usual social circle. For example, he might avoid spending time with Sasuke or Sakura because he is too preoccupied with his feelings about his parents.
Well, it could be a very emotional encounter. Naruto would be able to see his parents in their prime. His father, Minato, might give him advice on how to better handle his role as a Jinchuriki. His mother, Kushina, could cook for him, just like she always wanted to do for her son. They could also talk about the future of the Hidden Leaf Village and Naruto's part in it.
A plot for this type of fanfic could revolve around Naruto's inner turmoil. He could be constantly haunted by the question of why his parents neglected him. This could lead him to make some bad decisions, like getting involved with the wrong people. However, through a series of events, he starts to realize that he can create his own family and support system. He then begins to build a new life for himself, one that is not defined by his parents' neglect but by his own strength and the relationships he chooses to cultivate.
In this kind of situation, Naruto might first feel extremely sad and lonely. He could start by trying to prove himself to others. Maybe he'd focus on his ninja training more than ever, using it as a way to distract himself from the pain of being forgotten by his parents.