This viewer believes that the man has not gotten in touch with her again -that her longing imagination (spurred by repeated viewing of An Affair To Remember) has so taken over that she only fantasizes that he has left her (threw on the ground to a pursuing Deneuve an envelope containing) a note to meet him at the top of the Empire State Building on a particular day and time. The movie invites other viewers to instead believe that the man is simply cryptic and elusive, and has made such an appointment.
Fortunately for Deneuve's longing, she must go to New York for work (she is writing a book about a painter and must have three paintings currently in New York photographed for the book). While there, the photographer (Hurt playing a very goofy character) falls for her.
So, will she step into reality by taking up with Hurt who offers her love - or proceed further into the fantasy world by making her appointment at the Empire State Building? And if the latter, what will ensue? There are many inconsistencies in Deneuve's character - e.g., she has no sentiment about anything in her past - has just moved from her old home, has no desire to keep close relations with her daughter (and cleaned out her room), seldom attends reunions of the class where she knew the idealized Philippe - yet she aches with every couple she sees kiss and imagines Philippe everywhere.
Only reason to see this is for Deneuve -I'd never seen her play a character who can be rattled, silly, spontaneous - and she's wonderful. Hurt's character is however an idiot whom no woman would fall for - let alone both Paulina Porizkova (playing an art owner's wife involved with Hurt before her marriage) and Catherine Deneuve.
Finally, a warning to men: do not try Hurt's move with Deneuve at home. You will be injured.