She usually reacts with determination. Hermione is a strong - willed character. So, she immediately starts looking for evidence to prove her innocence. For example, in many fanfictions, she'll start by retracing her steps and making lists of who could have possibly framed her.
Hermione often gets angry when falsely accused. She's not one to take such injustice lying down. She might lash out at those who believe the false accusations at first. In some fanfictions, she uses her extensive knowledge of magic and Hogwarts to start her own investigation, while also trying to hold back her tears of frustration.
Well, Hermione typically reacts with a mix of emotions. At first, she's shocked that anyone could believe such false things about her. Then, she becomes very methodical in her approach to clear her name. She'll dig into old books, question witnesses if there are any, and use her logical mind to piece together what really happened. In a way, the false accusations fuel her to show the world that she's not what they wrongly think she is. This is seen in various fanfictions where she's put in this difficult situation.
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.
She often tries to ignore it at first. She's focused on her studies and doesn't want to give the bullies the satisfaction of a reaction.
Hermione may also start to scheme. She'll use her intelligence to come up with a plan. For instance, she might start to collect evidence against Snape, something that she could use to counter his blackmail. She'll research old school rules or find out secrets about Snape that she can hold over his head instead.
She might be angry at first. She has always been loyal to the Order's cause, and this abandonment would be a huge blow to her.
She could be conflicted. On one hand, she might be attracted to both in different ways. Sirius's charm and rebellious nature could draw her, while Remus's intelligence and quiet strength might also appeal to her. So she might struggle with her feelings, trying to figure out which, if either, she truly has deeper feelings for.
Well, Hermione could start arguing with Harry. She might say that he misread her actions or expressions. She could bring up past events to show that she has no reason to be jealous, like pointing out her own achievements and contributions which should make her above such petty feelings. And she may also question Harry's motives for saying so, wondering if he is trying to manipulate the situation or her emotions for some other reasons.
She might be shocked at first. Hermione is used to being seen as the voice of reason, so being called a hypocrite by Harry could leave her speechless for a moment.
Hermione would likely react with her characteristic intelligence and courage. She would probably try to use her vast knowledge of magic to find a way to escape or at least resist Fenrir. For example, she might try to use spells that could incapacitate him temporarily. She would also be likely to try and outwit him in conversation, looking for any weaknesses or loopholes in his plans.
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 great fanfiction where Hermione is falsely accused is 'The False Accusation'. In this story, Hermione is wrongly blamed for a potion mishap in Hogwarts. The author does a wonderful job of showing her struggle to prove her innocence and how her friends initially doubt her but then come around. It's a really engaging read.