One possibility is that Sirius would teach Harry all about his family's history in a more private and laid - back setting in France. He might introduce Harry to different magical cultures unique to France, like the Beauxbatons Academy. Harry could grow up with a more carefree attitude, away from the prying eyes of the British wizarding world.
Harry would likely be more confident. With Sirius as his sole guardian in France, he'd be away from the Dursleys' abuse. Sirius would encourage Harry to be bold and fearless, and without the constant pressure of the British wizarding community's expectations, Harry could be more laid - back and easy - going.
Well, he could be raised in a small, idyllic French village full of magic. The local wizards there might be more in tune with nature magic. So, Harry grows up learning how to communicate with magical creatures in the French forests in a way that's different from what he'd learn in Britain. Maybe there's a mystery about his parents in the French wizarding world too. Like, they were involved in some secret mission in France before they died, and as he grows up, he starts to uncover clues about it.
He'd probably be more refined in his manners, as French culture often emphasizes politeness and etiquette. His accent would be different, of course. And he might be more confident in expressing his emotions, as the French are generally more open about feelings. Also, his view of magic might be more influenced by French magical aesthetics, which could be more about elegance and style.
He could meet Fleur Delacour's family. Since Fleur is from France, her family might be an important part of the French wizarding community that Harry interacts with.
Another unique feature can be the settings. Some fanfictions might introduce French locations like the French Ministry of Magic or French wizarding villages. These new settings can bring in different types of magic, different magical creatures that are native to France, and different social structures within the French wizarding community. This all adds a whole new dimension to the Harry Potter universe that we know from the books.
He could meet French pure - blood families who have their own long - standing traditions. For instance, there might be a family that has a special connection to a particular magical forest in France. Harry might also run into French wizards who are experts in potion - making, as France is known for its fine potions in the wizarding world.
Well, one way could be through a magical accident. Maybe a powerful spell gone wrong transports Harry Potter to France and, due to some strange magic laws there, he ends up being proclaimed king. For example, if the spell disrupted the line of succession and the magic of the land recognized his powerful magic from Hogwarts as a sign of leadership.
Well, he might visit Beauxbatons Academy. Maybe he would meet some new friends there, like some interesting French wizards or witches. He could also explore the French wizarding culture, which is likely different from what he's used to in England.