One idea could be that in the fanfiction, Hinata is under the influence of a powerful genjutsu. This genjutsu makes her see Naruto as a threat to the Hidden Leaf village. So, she betrays him to protect the village in her distorted view. It could lead to a lot of inner conflict for Hinata once she realizes the truth and Naruto having to deal with the pain of her betrayal.
In these fanfictions, it might be related to the secrets Naruto holds. For example, if he discovers something about Konoha's dark past that certain people don't want exposed. They would then try to get rid of him by making him look like a traitor. Also, there could be external forces influencing Konoha to turn against Naruto, like other villages spreading false rumors.
One possibility could be that they are being mind - controlled. Maybe an enemy has found a way to manipulate them into attacking their own village. They might be used as pawns to create chaos in Konoha.
He might initially try to prove his innocence. He'll gather evidence or find people who can vouch for him. But as the situation worsens, he could become angry and more determined to find out the truth and expose those who are behind his false accusation. He might even leave Konoha to seek answers and allies elsewhere.
Hinata's betrayal could be a part of a bigger conspiracy. Maybe there are other forces at work in the ninja world that want to bring down Naruto. They use Hinata as a pawn. As the story unfolds, Naruto has to not only deal with Hinata's betrayal but also uncover the conspiracy and save the ninja world from a greater threat.
Sasuke would likely be very conflicted. He has a deep bond with Naruto, and he would not want to fight him, but he also has loyalty to Konoha. He might try to reason with Naruto first before taking any aggressive action.
Maybe a plot where there's a new student at Konoha High School who seems to be a threat to the harmony. Naruto, being the hero - like character, steps up to figure out what's wrong. Hinata, secretly in love with Naruto, supports him from the sidelines at first. But as the situation gets worse, she also joins in, and together they solve the mystery and in the process, their relationship blossoms.
Perhaps they are leaving together to search for a cure for some new and dangerous disease that has started to affect ninjas. They believe that by traveling the world, they will find rare herbs or meet wise sages who can help them develop a remedy. Naruto's determination and Hinata's knowledge of medicinal plants could be a great combination for this noble quest.
Some in the village would be sad to see them go. Naruto is a hero to many, and Hinata is also well - liked. People like Iruka would miss Naruto a great deal. But others might understand their need for a new life away from the village and support their decision.
The elders of Konoha could be the main antagonists. They are often shown to be power - hungry and willing to do whatever it takes to maintain their control over the village. They might see Naruto as a threat to their authority and decide to betray him. Another possibility is Danzo. He has always had his own agenda and has been shown to be ruthless in achieving his goals. He could easily be the one behind the betrayal of Naruto in a fanfic.