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.
One possible reason could be a misunderstanding. Maybe she was misled by false information about Naruto being a threat to the village. Another reason might be that she was under some kind of mind control. In some fanfictions, dark magic or evil entities can take over a character's mind and make them act out of character.
In some cases, Naruto might try to reach out to the Sakura he knows deep down. He could try to remind her of their past together, their training, and their shared experiences. He believes that the real Sakura would never do this, so he tries to break through whatever is making her act this way.
Well, in some fanfictions, Fu might use her unique jutsu skills. For example, she could create a powerful barrier to protect Naruto from Sakura if Sakura is somehow being controlled or acting aggressively. Fu's ability to manipulate nature energy could also play a role. She might use it to disorient Sakura or make her lose her focus on Naruto.
Since I haven't read this particular fanfiction, it's hard to say precisely. But if we consider common themes in fanfiction, Sakura could be a character from an existing franchise. 'Tries to move on' might imply that she is dealing with emotional baggage. For example, if she's from a anime or game, she could have witnessed destruction or had a falling out with friends. The fanfiction would then explore how she overcomes these emotions and progresses in her fictional life.
She could start by listening. Just being there to let Naruto vent out all the reasons for his hatred. Then, she might share her own wisdom. If she has some sort of special power or knowledge, she could use it to show Naruto that there's more to life than his hatred. For instance, if she can show him different futures or possibilities that don't involve him being consumed by hatred, it could be a start.
In many fanfictions, Naruto might use his ninja skills. He could suddenly appear and physically stop the bullies. For example, he might use his Shadow Clone Jutsu to surround the bullies and intimidate them into leaving Sakura alone.
Fu could use her healing abilities. If Sakura is attacking Naruto with some kind of harmful jutsu that causes internal damage, Fu can use her healing powers to counteract the effects. She could also transfer some of her own life force or energy to Naruto to keep him alive and stable while dealing with Sakura. This would be a more spiritual or mystical way of saving Naruto.