It ends up in a completely unexpected way with both of them starting to fall for... well...themselves
I assume that you're still looking for advice on writing this? There's a few big things that you should probably stress.
First of all, self loathing is a pretty common trait that's hanging around lately. It's really hard to see yourself without bias. So, having an identical copy of you show up, and realizing that person
isn't a total asshole is... Flattering. A real morale boost, right off the bat. That feeling could
easily lead to infatuation.
Secondly, there's a lot of little lies or deceptions that people like to lace into their lives. Maybe they only pretend to like or dislike certain things so they can hang out with their friends. Maybe they keep a secret so that they won't be a bother to others. Things like that... Things that a future self would
know about, even if they don't have a solution. Maybe for the first time in their life, they can afford to be "real" with someone. This could be especially moving if the reason they broke up with their ex is due to trust issues or deception.
Lastly, they'll have the same interests, so it would feel natural to go for the same restaurants, or the same hobbies. They can act like dorks or stress out over meaningless things together, because they know the other side understands and shares the sentiment. They have so much in common that it might be difficult to stop hanging out together. Like... they would be the worst kind of couple to be around. I honestly just gave myself a horrific sense of dread thinking about it from an outside perspective.
I think I'm done for now. Good luck~!
