He would probably be more conflicted. On one hand, he would have the potential for great good, like the original Harry. But on the other hand, he would have the shadow of Bellatrix's dark deeds hanging over him. This internal conflict could make him more withdrawn at times. He might also have a fascination with the dark arts, not in an evil way, but more out of a need to understand his mother's world. This would set him apart from the Harry we know, who was always more firmly on the side of light magic.
It could be stronger in certain dark arts. Given his parentage, he might have a natural affinity for curses and hexes that are associated with the dark side. He could learn and perform these spells with greater ease compared to other wizards. However, he might struggle with defensive and positive magic, like healing spells or protective charms.
Bellatrix's character would have to be rewritten to some extent. Saving Harry would go against everything she has stood for in the original story. So, she might become more conflicted, showing both her old, evil self and a new, emerging self that is capable of good. Her relationships with other Death Eaters would also be affected, as they would view her actions as betrayal. This would add a whole new layer of drama and complexity to her character in the fanfic.
Harry could become more secretive and distrustful. Growing up with Bellatrix, who is part of the Death Eaters and has a lot of secrets, Harry would learn to keep things to himself. He may not trust others easily, even those who seem friendly, as he has been brought up in an environment full of lies and hidden agendas.
He might be more feral. Growing up with a monster, he could lack some of the social graces that a normal upbringing in the wizarding world would provide. He may be more direct and less concerned with propriety.
He might be more laid - back. Canadian culture is often seen as more relaxed, so Harry could have a calmer demeanor. He wouldn't be as quick to get into arguments or be as impulsive as he sometimes was in the original story.
Harry might be more confident in his pure - blood heritage. Since Dorea Black would likely educate him about it, he wouldn't feel as out of place among the pure - blood families as he did in the original story. He may carry himself with more pride, but not in an arrogant way.
Harry might be more secretive. He'd have to hide any doubts or conflicting feelings he has about the dark path he's being led down. Bellatrix would not tolerate any signs of weakness or deviation from her plans. So, he'd become very good at hiding his true self, which would make his personality complex and full of contradictions.
He'd probably be more sophisticated. The Delacour family is known for their elegance and grace. Harry might have a more refined way of speaking and acting compared to his canon self. For instance, he would be more likely to use formal French wizarding greetings.
His personality would likely be more reserved and calculating. Growing up with the Malfoys, he'd be taught to keep his emotions in check and think before acting. He might be more aloof towards others outside of the pure - blood circle at first.
The story would become much darker. Bellatrix is a symbol of pure evil in the Potter universe.