In the fanfiction, it could be that Remus raises Harriet to be a strong advocate for the underdog. Since he has faced discrimination due to his lycanthropy, he would make sure Harriet has a big heart for those who are marginalized in the wizarding world. He might train her in non - violent forms of magic so that she can defend the weak without causing excessive harm. Also, their relationship could be a source of great emotional support for both of them, with Harriet looking up to Remus as a father figure and Remus seeing in her the hope for a better wizarding world.
She would likely be very empathetic. Remus, having faced so much hardship, would teach her to understand others' pain. So Harriet would be the kind of person who reaches out to those in need.
One possible plot could be that Harry grows up with a stronger sense of family. Sirius and Remus would teach him about his parents more directly. He might be more confident in his magic earlier, as they could start his training sooner. Also, he'd likely have a different view of werewolves and Animagi from an early age.
Perhaps a plot where Remus helps Harry with his Patronus charm much earlier. Since Lupin is an expert in Defense Against the Dark Arts, he could teach Harry advanced techniques. Harry might develop a stronger and more unique Patronus, like a wolf, influenced by Lupin. This could change the way he faces Dementors in his early years at Hogwarts.
Harry's personality would develop in a very different way. Growing up with Sirius and Remus, he'd be constantly surrounded by tales of the Marauders. This would make him more mischievous in a good way. He'd have a better understanding of the grey areas in life, as Sirius has a bit of a wild side and Remus has his own struggles. Harry would also be more independent, as Sirius and Remus would encourage him to think for himself and not blindly follow rules. He'd be more likely to question authority, especially when it seems unjust. And his sense of humor would be more developed, as Sirius is known for his jokes and pranks. Overall, he'd be a more well - rounded and confident young wizard.
He might be more reserved and empathetic. Remus is a rather quiet and introspective character, and Harry would likely pick up on those traits. He'd be more understanding of those with differences, like werewolves, given Lupin's condition.
Growing up with Remus would also expose Harry to a different side of the wizarding world. Remus has connections with various magical beings and outcasts. Harry would then be more open - minded about different magical cultures and species. He would not be as quick to judge based on what he has been taught at Hogwarts, but rather form his own opinions. This would shape him into a more well - rounded and worldly wizard compared to the Harry we know from the original series.
One interesting plot twist could be that Remus, being a werewolf, has to constantly protect Harry from those who fear his lycanthropy. This could lead to them having to constantly move, creating a nomadic lifestyle for Harry. Another could be that Remus teaches Harry different magic that is more in line with his own values, which might put Harry at odds with the traditional Hogwarts curriculum.
One key plot element could be Harry growing up with a different set of values. Remus and Sirius, being outcasts themselves, might teach Harry to question authority more. He'd likely be more in tune with the magical world's underbelly from an early age. Also, his relationship with Hogwarts could be different. Instead of the sense of wonder and discovery as in the original, he might approach it with a more jaded view, having heard stories from Remus and Sirius about their own school days.
The theme of good versus evil is prevalent as well. Harriet, like Harry, has to face dark forces. But in fanfiction, the nature of these dark forces can be different. It could be a new dark wizard or a more complex form of the existing dark magic. These stories often show Harriet's struggle to uphold the values of the wizarding world and defeat the evil, which is a classic and engaging theme in the Potter - inspired fanfiction world.