Adding height to a concrete slab

Back story: I have recently purchased an old house with an external garage in the Old Goodwood area. There is a French Drain built around the garage that catches most of the water, but during a heavy rain some water makes its way under the side door. The walls of the garage are brick columns every 8 feet with double walled brick in between and no wood framing.

What would be the best method of adding 2 - 4 inches of height to the slab to prevent water intrusion? Should I just install those speed bump size thresholds on all of the doors and cut the frames up an inch or two?