Hardwood floor to french door transition
I ran into the same thing. In some cases it looks OK for the wood to but up next to the threshold.  If the doors are metal, like exterior doors sometimes are, then they can't be cut. You have to remove the whole frame and raise them by adding a spacer underneath. I recommend pressure treated plywood. I have done one door and have 3 more to go. If they are wood and can be cut, the I would trim off the bottom of the doors to clear the floor plus a entry mat / rug.