Cover French Drain

I have an old home with a french drain/sump pump system inside. The holes in the cinder blocks are currently 0-2" above the floor grade, and have in the past been covered over with shingle material.
Much of this material is disintegrating (and blocking the drain)and needs to be replaced, or a new system needs to be setup (a caulked metal/plastic channel?). While I know I have some issues outside as well, I'm assuming the drainage inside isn't going to go away either, and needs to be repaired.
Any suggestions?
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