Wet blocks AFTER French drain and weep holes
It sounds like your water table is very close to the floor level. It's not necessarily damaging to the concrete, after all hydration is what actually cures concrete and concrete peirs are largely unaffected even after hundreds of years sitting in water. Lumber and your possessions in the house are of a concern. I would suspect that you would benift from at least a sump pump and even better, a weeping system tied into the sump pump.