The plot could revolve around Naruto and Jiraiya going on a secret mission together. During this mission, Naruto discovers more about his family's past through Jiraiya's knowledge. They might encounter an ancient evil that was known to Naruto's parents, and Naruto has to use the skills he's learned from Jiraiya to combat it.
It could be Orochimaru. Since he has a history with Jiraiya, he might target Naruto while he's under Jiraiya's tutelage, seeing Naruto as a potential threat in the future. Orochimaru could try to steal Naruto's power or use him in some dark experiments.
Well, one possibility is that Naruto could learn a great deal more about the past of the ninja world directly from Jiraiya. He might also get to witness some of the key events that shaped the present he came from. For example, he could be there when Jiraiya was gathering information on the Akatsuki, which would give him a huge advantage in dealing with them in his own time.
Jiraiya might comfort Naruto by sharing his own experiences. He could tell Naruto about the times he faced difficulties and how he overcame them. For example, he might talk about his training with the toads and how he grew stronger through perseverance.
Perhaps in this fanfiction, Jiraiya discovers that Naruto is going to be the cause of a major catastrophe in the future. He might have seen a prophecy or some sort of sign that convinces him Naruto has to die to prevent this. It could also be that Jiraiya has been misled by false information about Naruto, which makes him think that Naruto has become an evil force that needs to be eliminated.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he has reached a level in his training where he believes he needs new experiences and challenges that Jiraiya can no longer provide.
Well, in a way it depends on the context of the fanfiction. If the writer decides to give Naruto some sort of super - powered boost or if Jiraiya is weakened in some way. For example, if Naruto has some unique power - up that allows him to counter Jiraiya's toad - related jutsus easily. But Jiraiya is a very experienced and powerful shinobi too, so it's not a straightforward win for Naruto without some plot devices.
One great Jiraiya and Naruto fanfiction is 'The Mentor's Legacy'. It delves deep into how Naruto continues to uphold Jiraiya's teachings long after his death. It shows Naruto using the skills and wisdom passed down by Jiraiya in his battles and in his leadership of the village. Another interesting one is 'Jiraiya's Unfinished Business'. In this story, Naruto discovers some of Jiraiya's hidden notes and secrets that he left behind, which leads him on a new adventure to complete what Jiraiya started.
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.
Maybe Jiraiya found out some dark secret about Naruto's past, like his connection to the Nine - Tails, and decided to keep it from Naruto. When Naruto eventually discovers this, he would be angry at Jiraiya for not trusting him enough to share the truth. This could lead to a rift between them in the fanfiction.