I plan to install square nose against the threshold of my french door. The floor runs parallel to the door and there are door casings either side of the door.

After I cut the nose to 6-ft length, how should I treat the exposed wood just beyond the casings. A "round out" with quater circle seems an option---do I need to custom cut the round out or is there a pre-fabricated piec that I can purchase. Any other options or suggestion will be appreciated. Thank you in advance.

I often will cut a quarter circle at each end of a flat molding that will sit on top of the floor, such as that square nose or a reducer. I've seen other techniques to finish off the ends but none better or more "custom" looking than a hand cut curve. Smooth it with some fine sandpaper and a dab of poly. Everyone will be impressed.

I carry one of my wifes old nail polish bottles, with poly in it. I have some stain pens to colormatch.

That's a real good tip!