How did New Orleans get their name?

This is an euphemism for New Orleans, like the "Crescent City," that is attributed to Betty Guillaud, a gossip columnist for the Times Picayune, in the '70s as a term of endearment and an answer to the then I Love New York City hype. If it's the "Big Apple" then New Orleans is the "Big Easy," where everything is slower, simpler and easy-going.