He might be shocked. In the fanfic, if he sees things like his friends' future achievements or the new threats that emerge, it would surely startle him. For example, if he discovers that one of his friends has a family of their own and has become a great leader in the village, he would be proud but also a bit surprised at how much has changed.
With his usual determination. Naruto has always been one to face difficulties head - on. So, even if he's shocked by what he sees in the fanfic's future, he'll likely try to find solutions immediately.
Naruto has been through a lot in his own time, so he may use that experience to adapt to the past. He might start by making friends with the younger versions of people he knows. He'll also have to be careful not to reveal too much about the future to avoid disrupting the timeline. He could use his ninja skills to earn respect and find his place in the past world.
He might try to change certain events. For example, he could prevent some of the tragedies that occurred in the original story. Maybe he would stop the Uchiha massacre by warning the clan or finding a way to resolve the conflict between the Uchiha and the village leadership.
He would probably use his leadership skills. Naruto has grown into a great leader as Hokage. In the past, he could quickly assess situations and lead others, whether it's in a battle or in village - building activities.
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.
There are quite a few things. For one, he could teach past Naruto about the deeper secrets of the Uzumaki clan. Since Future Naruto has explored more about his heritage. He could also give tips on handling the Kyuubi's chakra more smoothly. Maybe some new jutsu combinations that he discovered over the years. And not to forget, how to better read an opponent's moves during a fight, which is a skill he would have refined over time.
Naruto could also meet the previous Hokages in their prime. He could learn from them directly and perhaps even influence their decisions. For example, he might be able to convince the First Hokage to handle the Uchiha clan's situation differently, which could have a huge impact on the future (or in this case, the future that Naruto comes from).
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.