Obviously Naruto would be one of the main characters interacting with him. Naruto would look up to Sarutobi as a mentor and a source of knowledge. Their interactions could range from training sessions to deep conversations about the future of the village.
Sasuke would also likely cross paths with Sarutobi. Sarutobi might try to steer Sasuke away from the path of revenge. He could offer Sasuke a different perspective on the Uchiha clan's history and the importance of the village as a whole.
In some fanfictions, the previous Hokages could be main characters in relation to Mirai Sarutobi. For example, the First Hokage Hashirama Senju's spirit could appear to give Mirai some wisdom or a special power. Or the Third Hokage, being from the Sarutobi clan as well, could have left some hidden knowledge that Mirai discovers, making the old Hokage an important part of the story.
Obviously, Naruto would be one of the main characters. And since it's about him being the son of Sarutobi, Sarutobi himself would be a crucial character. There would also likely be the usual Naruto characters like Sasuke, Sakura, Kakashi etc. as they would still be part of Naruto's life in the fanfiction, even with this new family relationship.
One of the popular characters paired with Sarutobi is Jiraiya. They are both important figures in the Hidden Leaf and their relationship, whether it's as comrades or as teacher - student in some fanfic interpretations, is always interesting to explore.
One possible plotline could be Sarutobi mentoring Naruto more closely. Since he's alive, he could pass on even more of his wisdom and jutsu knowledge to Naruto. For example, he might teach Naruto some of the more secretive fire - style jutsu that only he knows.
Hiruzen Sarutobi is definitely one of the most important. As the Third Hokage, he has a wealth of knowledge and power. His actions and decisions have a huge impact on the clan and the village. Another important character could be Asuma Sarutobi. He is a skilled ninja and his relationships with other characters, like Shikamaru, add depth to the fanfiction.
One consequence could be that the village runs more smoothly. With the paperwork out of the way, decisions can be implemented faster.
In this fanfiction scenario, Naruto might learn unique chakra control techniques from Sarutobi. Sarutobi, being an experienced ninja, could teach Naruto how to better manage his large chakra reserves. This would lead to Naruto being able to perform jutsus more efficiently and with less waste of chakra.
I really like 'Sarutobi's Unseen Trials'. In this fanfiction, it focuses on the political aspects that Sarutobi had to deal with in the Hidden Leaf Village. It gives a new perspective on his leadership and the difficult decisions he had to make.
Perhaps in this fanfiction, Sarutobi is trapped in a genjutsu created by a rogue ninja. Naruto, being highly resistant to genjutsu due to his Uzumaki blood, manages to break into the genjutsu world. There, he has to fight his own inner demons as well as the rogue ninja's illusions to free Sarutobi.
Perhaps he uses some ninja techniques like a shadow clone jutsu. He could make multiple clones to help him sort through and complete the paperwork quickly.