A villain that has the power to steal emotions could be a great choice. Imagine this villain targeting Edendaphne's friends and allies, draining their positive emotions. Edendaphne would have to find a way to not only stop the villain but also restore the emotions of those affected. It would be a very emotional and intense story.
Well, you could write a fanfiction where Edendaphne has to team up with a new character. They could have different personalities and powers, which would lead to some interesting conflicts and resolutions. For example, if the new character is really impulsive and Edendaphne is more cautious. Also, you could show how Edendaphne deals with the challenges of keeping her identity a secret, just like Ladybug and Cat Noir do.
A new character could be introduced as the main villain. Maybe a corrupt police officer who turns to the dark side. He could use his knowledge of the law and the city's security systems to commit crimes and frame the Miraculous heroes. He would be a formidable opponent as he has insider knowledge.
An evil alien warlord could be the main villain. This warlord could be bent on conquering Earth and other planets in the universe. He might see the Miraculouses as a threat and try to destroy Ladybug and Chat Noir first.
Hawkmoth is an obvious choice. His whole mission is to obtain the Miraculouses, and in a death fanfiction, he could succeed in a more devious way than in the original series, directly or indirectly causing Ladybug's death.
It could be a new villain created specifically for the fanfiction. Maybe an ancient sorcerer who was trapped for centuries and now wants revenge on the modern - day heroes. He has the power to turn things to stone and sees Ladybug as the main threat to his plans.
A possible main villain could be a character from Ladybug's past who has discovered her identity and is using that knowledge to create chaos. They could be blackmailing her or trying to steal her Miraculous by setting up elaborate mysteries and traps for her to solve.
Hawk Moth would be an obvious choice as he is the main villain in the series. He could be extra devious during Christmas, trying to ruin the festive mood for everyone in Paris. He might akumatize people who are feeling left out or jealous during the holidays.
The main villain could be a pirate captain who has found a dark Miraculous. He uses its power to control other pirates and turn them into his minions. He wants to use the power of the Ladybug and Cat Noir Miraculous to become the most powerful being on the seas.
Perhaps an outside force, like an alien entity, could invade the hero school. This entity could be attracted by the powerful Miraculous energy. It would be a very different kind of villain as it has no concept of the human values that the heroes at the school uphold, and it would take all of their combined skills to defeat it.
Ladybug and Chat Noir would likely be main characters as well. Since it's a Miraculous Ladybug fanfiction, they are important figures in that universe. They would interact with the son of the villain, either as enemies at first or as potential allies. And then there could be the villain parent. This character would have a big influence on the son's life and actions, constantly pulling him towards the path of villainy.