You can try a few things that can slow him down after you've seen that he's gone fast expand.
Generally if you are going an early scout against zerg, usually a 9 or 12 scout (9 scout is fairly safe vs a 6 pool) will let you know that they are going a fast expand. Once you have this information you can alter your build to counter what he is trying to do.
The goal of a fast expand is to take advantage of an early economy and generally out mine you and in turn out tech you and run you over. So how do you counter someone going for a heavy economic build early? Apply pressure.
With the early scout you can quickly drop a second and even a third barracks, or if you're really crazy and want to go all-in here's a 7 barracks build, specifically done on this map. You just go straight for the early aggression kill move.
Now if you aren't that crazy you can just go with an early 2 barracks pressure that puts down two bunkers at the base of his ramp and you load them with marines. You kill his expansion hatchery while denying his units from coming to help.
If you want to go more of a long game/safe route you can get a quick tech up to cloak banshee and punish his mineral line while you take your second base putting you back on even footing with them. This method is slightly more micro intensive on your behalf but will pay off in the end. This build uses a bunker and marines for an early defense while you tech up. This works for a few reasons:
Because of the map's architecture there is no way for them to reach your banshees unless they get mutalisks.
Unless they are playing really safe with an evolution chamber and spore crawlers they most likely won't have any detection which will allow you to run rampant in their base.
Because they went early expand they probably haven't gotten lair by the time you have cloak finished they won't have the ability to morph overseers, which is tied into the previous point of no detection.
These few methods should give you a fighting chance. The key to beating zerg as terran is to keep harassing them. A zerg cannot be allowed to expand as they please. If they are not punished, harassed, expansions denied, or otherwise constantly bothered, their economy will overwhelm you.