How real was the "droit du seigneur" and, if it was real at all, how did the Church dealt with the fornication and adultery sins commited by the Lord?

by RPL1985

When I was a middle schooler long time ago, I studied about the "droit du seigneur" or "jus primae noctis" (the right the Feudal Lords had to have the first sexual intercourse with his female subjects during their wedding night). For my (and my colleagues') contemporary sensiblities it seemed awful not for religion but for moral reasons.

Recently I read that this alleged right had been contested for quite some time and today it seems it's most discredited. Yet I also read some historians still argue it existed.
If it indeed existed, it must have had some far stretching argumentations to cover for adultery and fornication sins and their punishments, and how did Roman Church overlook it?

Ertata

Two answers by u/idjet and u/sunagainstgold cover this question reasonably well. Church did not overlook it because it did not exist as a legal right nor as a widespread customary practice.