It sounds like your house is positioned on a lot that has an extremely high water table. I believe the only way you can solve your problem is to find a way to keep the area around your home free of water. You will need a location Lower than your basement to divert the water too. You can do this by building culverts/swails around your home to divert the water. In addition I would recommend installing a second sump pump and possibly an emergency generator if you plan to use your basement.
It appears baased on the amount of water that you say you have french drains would not be the answer. You might also want to ensure that the water that you are pumping out is being sent far enough away sothat it is not returnning immediately.