He could be influenced by a powerful and mysterious force. This force might be something magical or a very strong jutsu that causes him to lose his memory and wander away from his family. In some fanfics, new and made - up powers can often play a role in such situations. Without his memory, he doesn't recognize his family and just drifts away.
His family would be extremely worried. Hinata, as his wife, would probably be in a state of panic. She might start searching everywhere for him, using all her skills and resources. His children would be confused and sad, constantly asking where their father is. And the rest of his family, like his friends who are like family, would also be on high alert and start looking for him right away.
Well, in fanfictions, often the plot takes a different turn. Naruto might hide from his family because there could be some sort of misunderstanding. For example, there could be false rumors about him being involved in something bad. And he might think that his family would believe those rumors without giving him a chance to explain. So, to avoid the immediate confrontation and judgment, he chooses to hide.
Naruto might rely on his ninja skills that he's learned. He's a resourceful character, so he'd use his stealth and combat abilities to find food and shelter. For instance, he could hunt small animals in the forest and build a simple shelter using his knowledge of basic survival techniques.
Perhaps he discovers something about his past or his powers that makes him feel he has to leave Konoha to explore it further. For example, he might find out about a hidden place related to the Uzumaki clan and wants to go there alone to uncover the secrets. Or it could be that he has some kind of internal conflict within himself, like feeling unworthy of being in Konoha due to some self - perceived failure, and so he runs away.
He could be running away because of false accusations within the family. Just like how he was wrongly judged by the village in the original story, if his family wrongly blames him for something he didn't do, like stealing a family heirloom or causing harm to a family member accidentally, he might choose to run away rather than face their unjust wrath.
The plot could take a very emotional turn. His family might be heartbroken and try to find him, which can drive a big part of the story. Meanwhile, Naruto himself could be going through a lot of self - discovery. He might become stronger or change in ways that are both positive and negative as a result of leaving his family. This can then have a huge impact on how he interacts with the world and the people he meets later in the fanfic.
However, it could also have negative impacts. He might start to feel lonely and bitter, which could lead to him making some bad decisions. He could be more easily influenced by the wrong people or ideas because he lacks the grounding that his family usually provides. Also, his relationships with his friends might become strained as he tries to keep them at a distance too, thinking that they'll side with his family.
Naruto might initially be heartbroken. He's a character who values family and connection deeply, so rejection would hit him hard. He could go into a state of self - doubt, wondering what's wrong with him.
One possible reason could be a misunderstanding. Maybe Naruto overheard something his family said that he misinterpreted as them not loving or believing in him. For example, if he heard them talking about his wild nature or his past mistakes in a way that he took the wrong way.