I think gauge does affect tone, but not as much as action. Generally, a high action means a fuller tone. Thicker strings also tend to give a fuller sound.
So if your guit has thicker strings and a high action, you must have a killer tone! But it's probably hard to play.
I guess the question is - why do you want a lower action? I know lots of guit players who want higher action to get better tone.
If you want a flatter neck to improve the feel, then as jony says, you might need to twist your truss rod to change the curve of the neck.
Personally, I'd see a pro about it if it is really causing you a problem. Try lighter strings first. If that doesn't help, then see a pro. I'm sure there are lots of recommendations on this site.