This is confusing.
How can a proposal be "...curiously rejected..."? It can either be rejected or accepted, the qualifier "...curiously..." seems strange.
Hiring a PI is done in secret, that's obvious and need not be specified in the logline.
What is the PI hired to investigate? Why she said 'no'? That is a very strange way to deal with rejection, possibly confront her, maybe ask her family and friends, but hiring a PI seems way off.
Why would the PI follow the wrong girl? He's not a very good PI then... Wouldn't the MC fire him once he finds out he's following the wrong girl? Otherwise, the premise makes little sense, why go along with an incompetent PI that's following the wrong person?!
I think that you're trying to imply that he lives in his own little dream world if so how is he going to go about learning the difference between truth and fiction - the action he takes is unclear.
Lastly, why would he want to get back together with a girl that rejected him? She said 'no' there's not much to win back, or am I missing something?