Naruto is devastated. He feels a huge void in his heart. Jiraiya was the one who believed in him from the start, and his death makes Naruto question a lot of things. He might even start to doubt his own strength for a while.
In fanfiction, Jiraiya's death can also be used to explore themes of sacrifice. He sacrificed himself for the greater good, and this can be further elaborated in different stories. For example, some fanfictions might show how his death inspired other characters to be more selfless.
One scenario could be that Jiraiya is poisoned before his fight with Pain. In the fanfiction, an enemy within the village who is secretly working for Pain's forces might have poisoned his food or drink. So, when he goes to face Pain, he is already weakened, and this ultimately leads to his death. Another possibility is that Jiraiya's death is a result of a time - traveling plot. If there is time - travel involved in the fanfiction, his actions in the past might accidentally create a situation where he has to die to preserve the timeline.
His character may become more withdrawn at first. Losing Jiraiya, who was like a father figure to him, could make Naruto less open and more focused on his internal pain.
Naruto might also isolate himself in certain fanfic scenarios. He feels that no one can truly understand the depth of his grief. He spends time alone, reflecting on all the things Jiraiya taught him and the memories they shared, like their time training on that toad -infested island.
At first, Naruto might isolate himself. He doesn't want to be around others as he is so consumed by his grief. He just sits in his room or goes to a quiet place where he can cry alone and think about Jiraiya.