He could be a powerful and respected shinobi from the Uzumaki clan. Given the Uzumaki's reputation for strong chakra and unique abilities, Naruto's grandfather might have been a key figure in the clan's history.
In this kind of fanfiction, Naruto might learn a lot of hidden family secrets. His grandfather could teach him some long - lost jutsu that was unique to their family. Maybe his grandfather would tell him stories about the early days of Konoha, which could give Naruto a new perspective on the village he loves so much.
If Naruto was raised by his grandfather, he might have learned different jutsu earlier. His grandfather, with more life experience, could have trained him better. Also, Naruto's relationship with the village might be different. He might be more respected as his grandfather could have a certain standing in the village, and this could change how people view Naruto from the beginning.
Perhaps Madara's grandfather was a diplomat of sorts for the Uchiha. He might have been involved in negotiations with other clans or villages. This would explain how the Uchiha managed to hold their ground and gain influence in the ninja world at that time. He could have used his wisdom and charisma to form alliances and avoid unnecessary conflicts.
This might be a story filled with the orphan's struggles and adventures before that fateful meeting. It could explore themes of identity and belonging. The encounter with the grandfather could change the orphan's life completely.
If Naruto meets his parents in fanfiction, one possibility is that they would be able to train him in ways that no one else could. Minato could teach Naruto advanced ninjutsu techniques, especially those related to the Flying Thunder God Technique. Kushina could help Naruto better control the Nine - Tails' chakra, as she was once its jinchuriki too. This meeting could also give Naruto a sense of belonging that he has always craved.
In such a fanfiction, Naruto might finally get to know his mother's personality. He could learn about her hopes and dreams, and perhaps she would share some family secrets with him. For example, she might tell him about the Uzumaki clan's special abilities that he hadn't known before.