The relationship between Jiraiya and Naruto would be quite special. Jiraiya would start by seeing Naruto as a project, a student to be molded. But as time went on, he'd see Naruto's unique spirit. Naruto would idolize Jiraiya from the start. Jiraiya would teach Naruto things that Kakashi couldn't. For example, Jiraiya could teach Naruto about the toads and their special powers. They'd probably have a lot of arguments too, because Naruto is headstrong. But these arguments would only strengthen their relationship in the long run. Jiraiya would also open up to Naruto about his past, his failures and successes, which would make Naruto trust him even more.
Their relationship would be very strong. Jiraiya would see Naruto as not just a student, but also as a connection to Minato. He would be strict but also very affectionate. Naruto would look up to Jiraiya as a father figure, since he never really had one. They would share many adventures together, with Jiraiya teaching Naruto about life, love, and ninjutsu.
In this fanfiction concept, it could lead to a really interesting dynamic. Jiraiya is a powerful and eccentric ninja. He could teach Naruto some really unique jutsu, like more advanced forms of Rasengan. And their relationship would be filled with Jiraiya's boisterous personality clashing and also complementing Naruto's determination.
Well, Naruto would probably learn a great deal more about the world of ninjas at a faster pace. Jiraiya was a very experienced and powerful ninja. He could teach Naruto some really advanced jutsu, like the Rasengan much quicker. Also, Naruto might grow up to be more like Jiraiya in terms of his attitude towards women, which could lead to some interesting adventures and misadventures.
One thing that could happen is that Naruto would learn a lot more about the toad sage mode earlier. Jiraiya could start training him right away. This would give Naruto an edge in battles. He would be able to use the toad - related jutsu more effectively and have a different combat style.
In this fanfiction, Jiraiya could be more open with Naruto about his past mistakes and love life. This would make Naruto see Jiraiya in a different light and might inspire him to be more cautious in his own relationships. Also, Naruto could be more protective of Jiraiya, knowing all that his master has been through. They would support each other not just in ninja battles but also in personal matters.
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.
His character would develop with a stronger sense of loyalty towards Jiraiya. He would inherit Jiraiya's values like protecting the weak and seeking justice. Naruto would also be more well - versed in the ninja arts and history due to Jiraiya's teachings. This would make him more respected among his peers at an earlier stage. Moreover, he might be more patient and less impulsive as Jiraiya could teach him the importance of thinking before acting.
Jiraiya would likely become more protective. He has always been a bit of a free spirit, but with a son in the picture due to time travel, he would be more cautious. His focus would shift from just his own adventures and spying to ensuring his son's safety and growth.
In this fanfiction, their relationship would be transformed. They would be like a married couple in a way, but without the formalities. Jiraiya would probably tone down his womanizing ways as he has a family to think about now. Tsunade would be more open and less prickly around Jiraiya. They would bicker less and cooperate more. Their relationship would be centered around Naruto, and as he grows, they would grow together as a family unit, with their bond getting stronger over time.
Naruto's character would become more cynical. He'd lose his usual optimism and be more distrustful of others. His sense of justice might be warped, as he now feels that he has been wronged. He could start to see power as the only thing that matters, rather than the bonds he once cherished.
Naruto's character develops through the training he receives from Jiraiya. He becomes more disciplined. For example, he learns to wake up early every day for training without complaining like he used to in Konoha. His ninja skills also improve, which boosts his confidence.