Well, Sirius Black could be an interesting character to put in a 'Harry Potter Dursleys fanfic'. Since he was Harry's godfather, his presence could stir things up for the Dursleys. He might be furious at how they treated Harry and take some sort of action. Hermione and Ron could also be included. They could visit Harry at the Dursleys' and be shocked at the living conditions. Their reactions and how they interact with the Dursleys could make for an exciting plot. And of course, the Weasley family as a whole. Their warm and loving nature would contrast greatly with the cold Dursleys.
Dumbledore would be an interesting addition. He has a lot of knowledge and power, and his interaction with Merlin would be fascinating. Ron could also be included for some comic relief and his loyalty would be an asset in any adventure that combines the two universes.
In many of these fanfics, there could be a new character introduced, like an old wizard who lives in the neighborhood secretly and notices Harry's situation. This character might play a crucial role in helping Harry deal with the Dursleys and his growing magical powers. He could be a mentor figure for Harry, guiding him through the tough times.
Definitely Dudley. In fanfic, he can be developed in so many different ways. He could become a wizard himself, or he could befriend Harry in a more meaningful way than in the original books. Another interesting character is Petunia. There could be more exploration of her past and her relationship with Lily, which can make her character more complex.
Obviously, Harry Potter and Nicolas Flamel are essential. But also including characters like Hermione Granger would be great. Hermione's thirst for knowledge would make her a perfect student of Flamel's teachings.
Akeno Himejima could also be a great addition. Her dual nature of being sweet but also having a darker side would create an interesting dynamic with Harry. They could have some really engaging conversations about power and morality.
Ron can also be included. He might be a bit clueless at first about their relationship, but then he can become a source of comic relief as he tries to play matchmaker or accidentally gets in the way of their romantic moments.
Obviously, Harry and Gabrielle themselves are essential. But characters like Hermione can add a lot too. She could be the one to help Gabrielle with her studies when she visits Hogwarts. Ron can also be there for some comic relief and to show the difference between the Hogwarts and Beauxbatons students.
Definitely Dumbledore. His wisdom would be crucial in guiding Harry and Maxima in any situation. Hermione would also be great as she could research and figure out how Maxima's powers work in relation to magic. And of course, Hagrid, who could introduce Maxima to the more unique and dangerous magical creatures in the wizarding world.
Neville Longbottom is a wonderful character to add. He has grown so much throughout the series and can be a great support to the trio. Dumbledore, even if in a ghost - like or memory form, can offer his great wisdom. Also, Draco Malfoy can be included in an interesting way. Maybe in fanfiction, he has a change of heart and teams up with the trio against a greater evil.
Hermione is always a great character to include. As a kid, she could be shown solving even more complex problems than in the books. Her intelligence and determination can drive the plot forward in fanfiction.