Naruto might initially be in shock and disbelief. He has always been loyal to the village, so being imprisoned for no real reason would be a huge blow. He would probably start by trying to reason with his captors, explaining that he is innocent. For example, he might say things like 'I've always protected this village, why would I do what you're accusing me of?'
One example could be a story where Naruto is framed for a crime he didn't commit by a hidden enemy within the village. This enemy manipulates evidence and convinces the village elders to imprison Naruto. Another could be a scenario where an impostor Naruto causes chaos and the real Naruto is wrongly accused and imprisoned as a result.
For Naruto himself, it often shows his growth. He might be initially angry and frustrated at being wrongly imprisoned. But as the story progresses, he could become more determined to clear his name and prove his worth. It can also strengthen his bonds with his friends as they try to free him.
There could be new characters created specifically for this fanfiction. Maybe a fellow prisoner who has some special knowledge or ability that helps Naruto during his imprisonment. Or a mysterious figure who is behind Naruto's false imprisonment, pulling the strings from the shadows.
In this fanfiction, Naruto might endure the false imprisonment with dignity at first. Then, as his godlike abilities start to surface, he could use them to not only free himself but also to reform the prison system if it's corrupt. He could use his power to expose the false accusations and bring justice to those who wronged him.
One possible reason could be a conspiracy within the village. Maybe some powerful and corrupt individuals in the Hidden Leaf want to get rid of Naruto for their own gains. They might frame him for a serious crime like treason or murder to eliminate his influence as a hero. Another reason could be a misunderstanding. For example, Naruto might be in the wrong place at the wrong time and there are false witnesses who claim he committed a crime he didn't. Or perhaps an enemy from outside the village has managed to create a false scenario that makes it look like Naruto is guilty in order to cause chaos within the Leaf Village.
In many such fanfictions, Naruto is initially hurt by the false accusations, especially if they come from his friends or the people he trusts in the village. But then, his strong will kicks in. He starts to analyze the situation carefully. He may talk to people who are neutral or try to find contradictions in the false accusations. He uses his ninja skills not just in combat but also in detective - like investigations to clear his name.
One example could be a fanfiction where Naruto is wrongly accused of stealing a powerful jutsu. In the story, perhaps a rival village's ninja frames him by planting false evidence at the scene. Another could be a situation where he is falsely accused of being a spy within his own village due to some misunderstandings and false testimonies.
There's a fanfiction called 'Naruto in Captivity'. In this story, Naruto is imprisoned by an old enemy who wants to use him for some dark experiment. The fanfiction is really good at building tension as Naruto tries to find a way out while also trying to stop the enemy's evil plans. The descriptions of Naruto's emotions and his internal battles are very well - written.
He could also be more resigned in some fanfictions. He might think about his past and how he's always been an outcast in a way, and see this imprisonment as just another hurdle. So, he would bide his time, waiting for a chance to prove his innocence.