One possibility could be Reverse - Flash. He could be interested in the Miraculous powers and try to steal them for his own evil purposes. He might see the power of the Miraculous as a way to enhance his own speed or gain new abilities.
A new villain created specifically for the crossover could be really interesting. This villain could be a scientist who has somehow harnessed the power of both the Miraculous and the Speed Force in a wrong way. He's bent on using this power to reshape the universes according to his own twisted vision. He has the ability to move at high speeds like The Flash and also use some kind of dark magic similar to Hawkmoth's akumas.
Perhaps it could be Hawkmoth working with a speed - based villain from The Flash's world, like Zoom. Hawkmoth wants the Miraculous for his own reasons as usual, and Zoom wants to prove he's the fastest by taking on The Flash and these new heroes. They could team up and create a lot of trouble for Ladybug, Cat Noir and The Flash.