Naruto would most likely continue to protect the village even after the betrayal. His sense of justice and loyalty to the place he calls home is too strong. He might even use their betrayal as motivation to become stronger and prove to them and everyone else that he is not the person they wrongly think he is.
He could also try to talk to them directly, despite the betrayal. Naruto has always believed in the power of communication and the bonds between people. He'd want to understand why they thought he was worthy of betrayal and try to convince them that they were wrong.
He would probably also feel angry. After all, he has sacrificed so much for the village and for them. He might start to question his own beliefs and values. But Naruto being Naruto, he would not give up easily. He would try to prove his innocence and show them that they are wrong. He could go on a journey to find evidence or seek help from other allies who still believe in him, like Shikamaru or Kakashi.
In such a fanfiction scenario, it could be due to a misunderstanding. Maybe there was false information spread about Naruto that made Jiraiya and Tsunade believe he had done something unforgivable. For example, an enemy could have framed him for a major crime against the village.
One possible plot could be that Tsunade and Jiraiya are deceived by false information about Naruto. Maybe they are made to believe that Naruto has turned to a dark side. For example, an enemy might have created false evidence of Naruto collaborating with a powerful evil force. Tsunade, being the Hokage, and Jiraiya, Naruto's mentor, would then be forced to take actions against Naruto that seem like betrayal from Naruto's perspective.
One possible scenario in this fanfiction could be that Naruto grows up with a more balanced upbringing. Tsunade might teach him medical ninjutsu and how to control his emotions better. Jiraiya, on the other hand, would surely train him in powerful combat techniques and in the ways of the sage. Naruto would probably be more mature and well - rounded at an earlier age, with a combination of Tsunade's tough love and Jiraiya's adventurous spirit guiding him.
Naruto would be determined to get to the bottom of it. He would not just accept the betrayal at face value. He would use his skills and the help of his friends to investigate what made Jiraiya turn against him. Naruto's ninja way is about never giving up, and this situation would be no different. He would fight against this betrayal, both physically if Jiraiya became an enemy in combat, and emotionally, trying to understand the reasons behind it all while still holding on to the hope that Jiraiya could be redeemed.
In this fanfiction, their relationship would be transformed. They would be like a married couple in a way, but without the formalities. Jiraiya would probably tone down his womanizing ways as he has a family to think about now. Tsunade would be more open and less prickly around Jiraiya. They would bicker less and cooperate more. Their relationship would be centered around Naruto, and as he grows, they would grow together as a family unit, with their bond getting stronger over time.
In the official Naruto story, Naruto is the son of Minato and Kushina. However, in the realm of fanfiction, it's possible for such a concept to exist. Fanfiction writers often come up with creative and alternative storylines. But this goes against the original Naruto lore. It would be a very different take on the Naruto universe, with implications for Naruto's character development, his relationships with other characters like Sasuke and Sakura, and the overall plot. For example, his training might be influenced by Tsunade and Jiraiya in a more family - oriented way rather than just as mentors.
One possible plot could be that Jiraiya is forced to betray Naruto due to some external threat. Maybe an enemy has captured Jiraiya's loved ones and threatened to kill them if he doesn't turn on Naruto. Jiraiya, in a difficult position, might have to pretend to be against Naruto to protect his loved ones while secretly trying to find a way to free both Naruto and his family from the enemy's clutches.
A possible plot could be that Naruto, under the care of Tsunade and Jiraiya, discovers new aspects of his heritage. Tsunade might know some secrets about the Uzumaki clan that she shares with Naruto. Jiraiya, being his godfather - like figure, helps him explore these new revelations. Meanwhile, the Akatsuki could still be a threat, and Naruto, with his new skills and knowledge, has to fight against them to protect the village and his loved ones.
In such a fanfiction, Naruto might receive more focused training earlier. Jiraiya could pass on his unique ninjutsu skills more intensively, and Tsunade might teach Naruto about medical ninjutsu. Also, Naruto would likely grow up in a more stable family - like environment, with the support and love from both Jiraiya and Tsunade. This could lead to him being more confident and less of an outcast in the village.