He didn’t sing that. The priest wrote his own lyrics for the couple.
However, I’m told the original has biblical meanings.
Cohen’s version has mixed Old Testament allusions in it. Samson suffered the cut hair and was bound having lost his strength, but David was beguiled by what he saw on a rooftop. Anyhow Cohen framed a semi-profane message with an exquisite tune and refrain, some think he did it as a joke, but the proverbial genie can’t be kept in the bottle.
The original has sexual meanings. It is an excellent song written by a talented songwriter, Leonard Cohen. But it doesn't belong in church. (BTW, it has come to be known as the Shrekellujah.)
I can't wait to hear Cohen's "I'm Your Man" sung from the altar. They could change a few words and everybody would swoon. "Oh, it brought me to tears!!!!"