In the traditional Batman comics, the relationship between Batman and the Joker is not a love story. It's more of a complex adversarial relationship. The Joker is a villain who constantly tries to cause chaos and harm, and Batman is dedicated to stopping him.
At first, Batman would be shocked and a bit confused. But quickly, his detective instincts would kick in. He would view the deaged Joker as a new and unexpected threat. He'd start gathering information about how the deaging occurred, in case it was part of a larger, more sinister plan. Batman would also be very careful not to underestimate the deaged Joker. He might try to isolate the Joker in a secure location to prevent him from causing chaos in Gotham. And he'd be constantly on the lookout for any signs of the Joker's old, devious self emerging from this new, younger form.