A story about the relationship of a depressed yet promising young woman who is about to jump but is saved by a mysterious ex-singer who was on the verge of jumping himself.

Coincidence I have just seen the trailer for. New movie based on the same concept.
http://www.imdb.com/title/tt0458413/

Completely right! Thank you, already changing it!

A premise with interesting possibilities, but so far there's only an inciting incident. After they don't jump, then what?

Specifically, what becomes the objective goal? What is at stake? What/who constitutes the antagonist? Which character is the protagonist?