Have you tried locking and unlocking the doors before trying the inside handles? If this doesn't work you must have the childproof locks activated, which means the inside door handles won't open the doors and since you have removed the only handles that will work, you have created a real problem and may have to seek a professional to get the doors to open?
You re-installed the door handles improperly. The part of the handle opposite the lever never fully clipped into the handle rod mechanism. I've encountered this problem before while wrapping cars, take the handle off, and re-install it. Usually what happens is the mechanism un-clips from the door panel, so when you shove the handle back in, it doesn't grab the mechanism and lock into place.
The Cruze uses a euro-style door handle. The rear of the handle hooks over a small lever which operates the latch. With the exterior handle removed, you should be able to get your pinkie finger in the hole where the rear of the handle goes in and feel the lever that the handle pulls. You might have to use some kind of hook tool (maybe a bent coat hanger) in that hole to reach the lever if it's too far in. Pull the lever toward you and it should release the latch.