It could be an ancient demon that was sealed away long ago but has now been released. This demon has the power to manipulate time and space, which makes it a formidable foe for both heroes.
An organization that opposes the hero's unorthodox methods could serve as the antagonist. They might believe in a more traditional way of heroism and see the hero as a threat to their established order. They could try to stop the hero from using their unique abilities or ways of doing things.
It could be a modern - day villain who wants to use the power of the ancient heroes for his own evil purposes. He might be jealous of Percy's connection to the ancient heroes and try to stop him at every turn.
It could be a rogue demigod who has a vendetta against Percy. This demigod might have spread the false rumors that led to Percy's banishment in the first place, and now he wants to make sure Percy never returns. He uses his own powers and manipulates other demigods and monsters to achieve his goal.
It could be a demigod who was once a hero but became corrupted by power. Maybe they were overlooked for some big honor at Camp Half - Blood and now they seek revenge on Percy and the other heroes. This character could have powers similar to Percy's but use them for evil, like causing tsunamis to destroy coastal cities instead of protecting them.
It could be a new villain who has the power to manipulate time. This villain would be constantly changing the past and future to create chaos in Paris. Chat Noir would have to figure out how to stop this power. Maybe the villain is doing it to find a powerful artifact from the past that was hidden to prevent it from being misused.
It could be All For One. He might see the 'Villain Class 1A' as a useful tool to further his own evil plans. He could manipulate them into doing his bidding, which would put them in direct conflict with the heroes, including Class 1A.
It could be a rogue scientist. They might be jealous of the natural quirks that people are born with and decide to steal them to create artificial super - beings. They would be highly intelligent and use their scientific knowledge to develop devices or techniques to steal quirks.
It could be a powerful villain who sees Naruto as a threat to his plans in the My Hero Academia world. Maybe a villain who wants to use Naruto's unique abilities for his own evil purposes and when Naruto refuses, becomes his enemy.