Should I talk to him or just let it all fall naturally?

If you have been seeing each other at the gym all the time for a year and he hasn't tried to speak to you and you have only actually made eye contact once then it really doesn't sound like he likes you at all. Just because he smiled at you once really doesn't mean anything, when you catch the eye of someone who is looking at you the normal thing to do would be to smile politely. So yeah try talking to him if you want but waiting for things to "fall into place" seems like you'll be waiting forever. Nothing ever falls into place until you put it there.

Something that I see done quite a lot is people (usually women approaching men) pretend to ask them a workout related question, such as, "Hey, do you think I have the form right with this move?" and try from there to start a casual conversation. If you want to do this, try not to interrupt his workout, it might be best to do it when he's finishing or finished and about to leave. Also pay attention and make sure that it doesn't look like you just singled him out in a crowd - make your act plausible.

Remember, though, he might not be interested. A fitness center is the second most dense center of attractive young people behind modeling agencies, and a LOT of the patrons are used to getting some kind of attention from the opposite sex.