Well, in a fanfiction where Naruto travels to the past, he could meet his parents when they were young. He could also learn new jutsu from the past ninjas that were lost over time. Maybe he'd even be able to influence the early development of the Hidden Leaf Village in ways that would make it stronger in his own time.
Naruto would meet his younger self. This would be a really strange situation. He could also meet all the important shinobi from the past. For example, the First and Second Hokage. He might have a chance to learn from them directly, instead of just hearing about them in stories. Additionally, he could meet some of the characters who were only mentioned in passing in the original story but had a big influence in the past.
In such a fanfiction, Naruto might try to prevent some of the tragedies that occurred in the past. For example, he could stop the Uchiha massacre. He would use his knowledge from the future to change things. Maybe he'd also be able to save some characters who died early in the original story, like Jiraiya. And he could potentially have a huge impact on the relationships between different clans, as he'd know about future conflicts.
Jiraiya. Naruto could have a different kind of apprenticeship with Jiraiya. He could share some of his future experiences with Jiraiya, which might change how Jiraiya trains him and also how Jiraiya approaches his own missions and prophecies.
Naruto's character could develop in many different ways. If he travels to the past, he'd have to adapt to the different ways of the old ninja world. He might become more respectful of the traditions as he sees how they were formed. Also, he could become more of a mentor figure to the younger versions of his friends, which would change his self - perception from a student to a teacher, thus making him more mature and responsible.
One interesting plot could be Naruto using his future knowledge to prevent the Uchiha massacre. He might try to change Itachi's situation and find a way to resolve the conflict between the Uchiha clan and the village without all that bloodshed.
Naruto's character might develop a greater sense of responsibility as he realizes the impact of his actions in the past on the future. He may become more patient, knowing that he has to tread carefully to avoid major disruptions.
He could meet an AU version of Hinata who is more assertive and outgoing. Maybe she's a powerful ninja in her own right and not as shy as in the original story.
Naruto may run into some friendly space explorers who are amazed by his ninja skills. They could help him navigate the strange new world of space and introduce him to advanced technologies that are different from what he's used to in the Hidden Leaf Village. There might also be some wise, old beings in space who can teach Naruto new ways to master his chakra.
He'd probably be super surprised. I mean, seeing yourself as the opposite sex is not something that happens every day. He might blurt out something like 'Who are you? You look like me!' and then start to realize the situation. He could be a bit embarrassed too, especially if female Naruto had some different mannerisms or ways of dressing.