Perhaps Fleur uses her magical skills. She could cast a spell to create a diversion, like making the Dursleys believe there is a dangerous magical creature in their house. While they are distracted, she grabs Harry and whisks him away to safety. She might also use a charm to make the Dursleys forget about Harry so they won't try to stop him from leaving.
In some fanfictions, Fleur might use her Veela charm to intimidate the Dursleys into letting Harry go. The Dursleys, being easily cowed by the extraordinary, would be no match for Fleur's alluring yet powerful presence.
Fleur could be shown as more independent and brave. Since she's taking it upon herself to save Harry, it shows her courage. Maybe she becomes more confident in her own abilities outside of the Triwizard Tournament context.
Well, perhaps Fleur uses her Veela charm to intimidate the Dursleys into letting Harry go. She could arrive at Privet Drive in a blaze of magical beauty and power, and the Dursleys, being the cowards they are, would be too scared to oppose her when she demands Harry come with her.
Charlie could use magic to simply apparate Harry away from the Dursleys' house. It's a quick and efficient way to get Harry out of that horrible situation.
Perhaps Snape uses magic to create a distraction at the Dursleys' place. He could make strange noises or apparitions that scare the Dursleys, and while they are in a panic, he grabs Harry and disapparates. This would be a quick and efficient way for him to rescue Harry.
Maybe Percy uses his magic skills to create a distraction. He could conjure up some strange creatures outside the Dursleys' house. The Dursleys, being afraid of all things magical, would be distracted long enough for Percy to sneak in and get Harry out.
Well, he could use his magic skills secretly. Maybe he casts a spell on the Dursleys to make them docile or distracted long enough to get Harry out. For example, he might use a Confundus Charm on them so they don't notice Harry leaving.
In the fanfic, Snape might use his knowledge of the Dursleys' house layout. He may enter the house unnoticed, find Harry, and then use a Portkey to quickly get them both out of there. He could also have some sort of charm or potion that he uses to counter any magic the Dursleys might have used to keep Harry there, like a spell - breaking potion. And he may have planned the whole rescue very carefully, choosing a time when the Dursleys are least likely to notice, like in the middle of the night.
Well, in some fanfic scenarios, Voldemort might have made a deal with someone who has access to the Dursleys' house. For example, he could have bribed or threatened a neighbor or someone who works in the area. Then, when the time is right, he enters the house under the guise of this person's help and rescues Harry. It could also be that Voldemort has some sort of inside knowledge about the protective spells around the Dursleys' place. He finds a loophole in those spells and slips in to save Harry.
In this fanfiction scenario, Bellatrix saving Harry from the Dursleys is quite an unexpected twist. It could be that Bellatrix has some ulterior motive. Maybe she wants to use Harry for her own dark purposes against Voldemort. She might see Harry as a valuable pawn in the power struggle within the Death Eater ranks.
It could be out of loyalty to the wizarding world. Harry is seen as an important figure in the fight against the dark forces. Fleur realizes that Harry's safety is crucial for the future of the wizarding community, so she saves him from the Dursleys who are a threat to his well - being in a different way compared to the dark wizards.