The sump pump may work, but you still might get water on the finished side of the basement, depending on soil conditions. A sump pump, though, is only part of the system.
If you only break the floor and install the sump in one area, it will absorb the water from that area (if designed in a gravel bed). If the water is primarily entering from the finished side of the basement, the hydrolic pressure can push it right through the concrete. It does not need a crack. In a real wet season, concrete leaches water from one side to the other, like the wick on a lamp. With the added hydrolic pressure, (1' of water column = 1/2 pound of water pressure) water is able to find those spaces in the concrete you can not see with your eye.
The reason for a french drain system (drain tile), is it runs the perimeter of the concrete and prevents the water pressure from building up on any one side.