Well, obviously, the relationship between the Potters and the Malfoys becomes extremely hostile. The Malfoys would see the Potters as thieves who stole Harry from them. For Harry, his view of the Potters might be initially one of confusion. He was with the Malfoys, and now he's with the Potters. But over time, he might come to see them as his true family.
In this fanfiction scenario, the relationship between Dumbledore and the Potters could be strained. Dumbledore might have had some sort of plan involving Harry and the Malfoys, and the Potters' kidnapping of Harry throws that plan into chaos. And for the Death Eaters, they might see the Potters as a bigger threat now. They could target the Potters more aggressively, not just because of their opposition to Voldemort, but also because of this act of taking Harry from the Malfoys.
One possible motive could be that the Potters discovered some dark plot by the Malfoys involving Harry. Maybe they found out that the Malfoys were planning to indoctrinate Harry into their pure - blood supremacist ideology against his will. So, to protect Harry from that, they kidnapped him.
In the original Harry Potter novel, there was no plot of Harry being kidnapped by Malfoy. Harry and Malfoy did not see eye to eye at Hogwarts, but there was no kidnapping. Harry Potter and the Goblet of Fire was not enough. Everyone, please click to read the novel!
Obviously, Harry Potter and Draco Malfoy would be main characters. Harry, whose perspective is changing towards the Malfoys. And Draco, who represents the Malfoy family and all its associated traits and values.
Obviously, Harry Potter himself is a main character. He's at the center of many of these fanfictions, whether it's about his growth within the family or his relationships with other family members.
He might change in terms of his magical abilities. Maybe the Malfoy family focuses on different types of magic than what Harry was exposed to in the original story. So, he could be more proficient in dark arts - adjacent magic, but also struggle with the moral implications of using such magic. He may have to reevaluate his own identity and what it means to be a 'good' wizard.
In fanfiction, Harry's understanding of the Potters can expand. He might see his parents as more complex characters. For instance, if a fanfic shows James Potter as having a struggle with a certain type of magic, it makes him more than just the heroic figure Harry knew. This changes Harry's view of his father.
Perhaps there's a plot against Harry by some dark forces, and the Potters believe that only they can protect him properly. They might think that the people who have been taking care of Harry so far are not equipped to handle the new and more dangerous threats. Also, it could be that the afterlife in the wizarding world has some rules or opportunities that allow them to try and get Harry back into their family fold. They could have been given a second chance, so to speak, and are eager to take it.
Another way is through a shared danger. Suppose there's a new threat in the wizarding world that endangers both Slytherins and Gryffindors. Malfoy and Hermione, along with Harry, have to put aside their differences. In the face of this danger, Malfoy might have a change of heart and begin to respect Hermione. Their relationship could develop from grudging allies to something more like friends. This could be a slow process, with many bumps along the way as they both struggle to let go of their preconceived notions.
He becomes more conflicted. Growing up as Lucius Malfoy's son, he is exposed to different values. So, instead of the Gryffindor - like straightforwardness, he may have a more calculating side.
Well, their relationship is complex. In the beginning, Draco may try to bully Harry as he used to in Hogwarts. But as Harry shows his true self and they spend more time together, Draco realizes that Harry is not the enemy he thought. They might start sharing secrets, and their relationship could evolve into a sort of brotherly bond, where they protect each other from outside forces and also from the expectations of their respective 'sides' in the wizarding world.