Naruto could be a bit hesitant at first if the situation is really complex or dangerous. He might need to think about the implications and if he is truly capable of helping. But in the end, his loyalty to Sakura and their friendship would likely make him agree. He might say something like 'Sakura - chan, don't worry. I'll do whatever I can.'
Another possibility is that Naruto is in the middle of his own mission or struggle. So, his response could be to ask Sakura to wait a bit while he arranges things. He would assure her that he will come to her aid as soon as possible. He might also start gathering resources or allies that he thinks could be useful in the situation that Sakura has presented to him.
In some fanfictions, it could be a situation involving a curse or a dark magic that Sakura doesn't understand. She has exhausted all her medical and ninja knowledge but to no avail. Naruto, on the other hand, has had experiences with all sorts of strange and powerful forces, so she begs him for help in order to save someone or something she cares about.
He could also try to dodge her attacks while still trying to reason with her. Naruto has a strong sense of loyalty and friendship, so he would likely be very reluctant to fight back against Sakura. He might keep asking her why she's doing this and try to get through to her emotional side.
Sakura might be hesitant. She could say that she needs time to think. She values Naruto as a friend and is suddenly faced with this new revelation, so she wants to be sure of her own feelings before giving an answer.
Naruto could respond with anger at first. He has given so much to the Leaf Village, and this betrayal would be like a slap in the face. However, his kind heart might also make him wonder if there is a misunderstanding. So, he could start by trying to communicate with the villagers he trusts. If that fails, he might leave the village for a while to get stronger and then come back to confront those who wronged him.
Naruto might become more confident in the 'naruto does know sakura' fanfiction. Since he knows Sakura's feelings, he no longer has to wonder about her and can focus on other aspects of his life. This new - found knowledge could also make him more empathetic towards others' hidden feelings.
She might be confused at first. Sakura is used to Naruto being friendly and now his coldness would be a big change. She may start to question what she did wrong.
Naruto might be very forgiving right away. He has always had a big heart and cared deeply for Sakura, so he could just accept the apology with a big grin and say it's all in the past.
Naruto could also feel a deep sense of hurt. After all, he has been through a lot with Sakura. In the face of her betrayal, he might start to question his own judgment of people. However, being Naruto, he would not give up easily. He might try to find a way to redeem Sakura or at least make her see the error of her ways. He would draw on his own experiences of being ostracized in the past and use that to try to understand her actions and find a solution.
Sometimes, in fanfiction, Naruto stands up to Sakura when it comes to her attitude towards Sasuke. Sakura might be blindly following Sasuke's every move, and Naruto, having a more objective view of Sasuke, could confront Sakura. He would tell her that she should value herself more and not just revolve her life around Sasuke. Naruto has his own understanding of friendship and loyalty, and he would use that to make Sakura see things differently.
Perhaps Sakura is overly critical of Naruto in the fanfiction. She might focus on his flaws and not give him any credit for his achievements. Naruto, who has always been striving for recognition, especially from Sakura, would be deeply affected by this. Her constant criticism could chip away at his self - esteem and cause him to sink into depression.