Harry would likely start off as a rather arrogant character, given the Malfoy upbringing. He'd look down on those he considered beneath him, like muggle - borns. But as he experiences different things, he could start to question his family's beliefs. Maybe he meets a kind muggle - born witch or wizard who shows him that there's more to a person than their blood status. This could lead to a gradual change in his character, from a pure - blood supremacist to someone who believes in equality.
One possible development is that Harry would be extremely conflicted. On one hand, he has the loyalty to his family, the Malfoys. On the other, he might start to see the wrongdoings of the Death Eaters. His relationship with his father, Lucius, would be complex. Lucius would expect Harry to follow in his footsteps, but Harry could have his own ideas. He might develop a secret friendship with someone from the 'opposite side', which would cause him a lot of internal turmoil as he tries to keep it a secret from his family. His magical abilities might also develop in a different way. Instead of the traditional Gryffindor - like courage, he might learn to use his Slytherin cunning in a positive way to help those in need.
In this fanfic, Harry's character could develop in many ways. At first, he would be very much influenced by the Malfoy name and the power and prestige associated with it. He'd be confident, but in a more haughty way. As the story progresses, if he discovers some dark secrets about his family or the Death Eaters, he could become disillusioned. His development might involve him trying to break free from the expectations of his family. He might start to explore different aspects of magic that are not approved by the pure - blood society. His view of the wizarding world would change drastically, from one of pure - blood superiority to a more inclusive view, and this would be a long and difficult journey for his character.