French drain inside basement

I have my basement usually dry. However, in one wall there is about 1" diameter hole from outside made just at the floor level. Then there is very ugly and uneven groove made in concrete floor that goes from the hole along the wall to the sump pump pit that is located near the same floor about 8' away. I never saw water coming out from the hole. However, when we have heavy rain water starts to sip from the groove itself (probably the groove is not seal properly). I am currently finishing my basement and I really don't know how to best address this problem. Although I never saw water coming out of the hole I am afraid of patching and blocking it. If it was maid there was probably a reason and the reason was probably to release hydrostatic pressure from outside the house foundation. But I need to deal somehow with the groove in the concrete floor. Again I don't want to level it with cement as if water ever comes through the hole it will just stay in basement as there will be no way to direct it to sump pump pit. I thought about constructing somewhat like a French Drain just from the hole to the sump pump. I will break a trench in concrete floor from the hole to the pit. I then put probably perforated PVC pipe sloped from the hole to the pit and then pour cement over it to level the floor. So if water comes through the hole it will flow via the sloped pipe to the pit. Does this sound a right plan?