One plot idea could be that she grows up learning the unique magic and culture of the Delacour family. Maybe she has a special bond with Fleur and they train together for some wizarding tournament. Another idea is that she discovers secrets about her past that are different from the original Harry Potter story because of her upbringing by the Delacours.
Well, it could involve Harry growing up with the Delacour family's unique culture. Maybe he'd learn different kinds of magic that the Delacours are known for. He might also have a different personality, influenced by their flamboyant and refined ways.
He'd probably be more refined. The Delacours are a posh family, so he might have better manners.
In the fanfiction, it could be interesting if Harry uses his magic to protect the other orphans from bullies. He might not fully understand his powers yet, but his instincts kick in. And then when he finally gets his Hogwarts letter, the other orphans are both sad to see him go but also excited for him, and he has to figure out how to leave the only home he's known while also being eager to enter the wizarding world.
One idea could be that Harry grows up with cat - like reflexes and stealth. He might be able to move around Hogwarts unnoticed more easily, like a cat prowling in the shadows.
One interesting plot could be how Harry's magical abilities are perceived in a world of nations. Maybe he uses his magic to solve international disputes. Another idea is that different nations try to influence his upbringing, each adding their own cultural and magical elements to his training.
One idea could be that she has unique magical abilities due to her demon - raised upbringing. For example, she might be able to communicate with dark creatures in a way normal wizards can't. Another could be that she struggles with her identity, being part of the wizarding world but also having this demonic influence. She could also face a lot of prejudice from the wizarding community who fear her because of where she was raised.
One possible plotline could be Harry learning the unique culture and magic of the Delacour family. For example, he might be exposed to different types of French magic that he wouldn't have encountered otherwise. Another could be his relationships with the Delacour sisters. Maybe he forms a really close bond with Fleur, like a brother - sister relationship, which changes the way he views relationships in general. Also, his upbringing by the Delacours might give him a different perspective on the wizarding world politics, as the Delacours could have their own views and influence on him.
She would likely have a different view of family. Growing up with the Delacours, she would have a more flamboyant and loving family environment. This would make her more confident in showing affection and relying on family support. In contrast, the original Harry had a rather lonely childhood until he discovered the wizarding world. Her relationships with others would also be different. She might be more diplomatic, having learned from the Delacour family's social skills, which could lead to different interactions with characters like Snape or Dumbledore.
One idea could be that Harry grows up with a very different set of values. House elves are known for their loyalty and hard work. So, Harry might be more in tune with serving others selflessly. For example, he could be more eager to help his classmates with their problems without expecting anything in return.
One idea could be that Harry, in his Animagus form from a young age, has a unique bond with the magical creatures in the Forbidden Forest. They protect him and he learns their ways, which gives him an edge when it comes to dealing with dark magic later on.