SPOILER ALERT!
I haven't read the book, either way, I don't think I would read it cuz I'm more into movies than books, but I really think that not everybody gets the way Finch was seeing his life, maybe that day in the ledge of the bridge he was about to jump too, maybe they saved each other or maybe all the things that he did in the school were on purpose cuz he already knew he ain't gonna make it, maybe all he was trying to do was finding something good to do for another person and he realized when he met her.
Maybe if he hasn't died you wouldn't get it the message.
Like a say, all those maybes probably are true or probably not but that's the magic of the movie, dreaming and wondering about the possibilities of Finch's life.
By the way I'm not happy with his death, but that how it goes.
PD: I think he already knew, what he gonna do, but the way to let his mark along the path was changing her life and showing the true meaning of life.