Well, it could be that they're working on a difficult potion and there's an accident. Maybe the potion explodes and they both get covered in it. As a result, they start having strange visions of each other's pasts. Draco sees Hermione's struggles as a Muggle - born in the wizarding world, and Hermione sees Draco's family pressure. This new understanding of each other could lead to an unexpected friendship or at least a truce between them.
One possible plot could be that during a potions class, Draco and Hermione accidentally mix the wrong ingredients. This could lead to a magical reaction that causes them to swap personalities. Hermione might start acting like Draco, being more aloof and sarcastic, while Draco could become more studious and rule - abiding like Hermione. They then have to figure out how to reverse the effect while also dealing with the chaos it causes in Hogwarts.
In a fanfiction about Hermione's potions accident, perhaps she was trying to create a new potion for a school project. But she misread a step in an old, dusty potions book. As a result, the potion explodes and creates a time - warp effect in the potions classroom. Now Hermione has to deal with different versions of her friends from different time periods all while trying to fix the potion to set things right.
It could improve their relationship. After the accident, they might realize that they have more in common than they thought. For example, they both are very determined when it comes to potions, just in different ways. This newfound understanding could lead to a grudging respect and the start of a friendship.
A great plot point could be that the potions accident results in them being able to read each other's minds. They suddenly have access to each other's deepest thoughts and secrets. This makes them extremely uncomfortable at first, but as they start to understand each other better, they form an unlikely bond. For example, Harry discovers that Draco is under a lot of pressure from his family, and Draco realizes that Harry has his own insecurities despite being the 'Chosen One'.
One possible scenario in such a fanfiction could be that during a potions class, Harry and Draco are forced to be partners. They are making a complex potion, and due to their mutual dislike and lack of proper communication, they mess up the ingredients. The potion explodes, covering them both in a strange goo. This accident could be the start of them seeing each other in a different light, perhaps realizing that they are not so different when it comes to making mistakes.
One popular one might be 'The Unforeseen Consequences' where the potions accident leads to them having to work together closely to reverse the effects. It has a great plot that delves into their characters.
Professor Snape might also be involved. Despite his usual strictness with Hermione, he is a potions master. He could see this as an opportunity to teach her a lesson about being more careful, but also help her because he wouldn't want a student to be in real danger from a botched potion. And there's always the possibility that Dumbledore, with his vast wisdom and knowledge of magic, could offer some cryptic advice that ultimately helps Hermione solve the problem caused by the accident.
One possible plot could be that Draco, for some reason, becomes Hermione's servant. Maybe it's part of a magical pact or a punishment from the wizarding world. Draco, being used to his pure - blood superiority, would initially resist but gradually learn to respect Hermione's intelligence and kindness. They could then go on adventures together, facing various magical threats and learning more about each other's true natures.
The plot could start with Draco and Hermione realizing their mutual attraction despite their initial animosity. They might secretly plan their elopement to avoid the scrutiny and opposition from their friends and families. Maybe they find a magical place, like an ancient forest where they exchange their vows in a private ceremony.
A possible plot could be that Hermione is getting ready for a big wizarding event and her bra has some sort of magical enchantment on it. Draco accidentally discovers this when he's snooping around (he's still a bit of a troublemaker in this scenario). This discovery leads to a series of events where they have to work together to figure out who enchanted the bra and why. It could be part of a larger plot to embarrass Hermione or to gain some sort of magical advantage.
It could also be that Draco discovers a new and powerful potion recipe that he wants to share with the wizarding world through his shop. But there are those who want to steal the recipe from him, so he has to protect it while also running his business. This would lead to a lot of adventure and mystery in the fanfiction.