To the great surprise of French pop-rock band Phoenix, the group’s 2009 album, Wolfgang Amadeus Phoenix, became an international success.

Following four far-less popular albums, Phoenix — singer Thomas Mars, guitarists Laurent Brancowitz and Christian Mazzalia, and bassist Deck D’Arcy — didn’t have much to be encouraged about regarding Wolfgang Amadeus Phoenix’s commercial prospects.

“When we recorded the album in Paris, a few friends came over to the studio,” Mars recalled from his home in New York. “They were surprised by the sound of it. They didn’t really like it.”

What’s more, Phoenix had neither management nor a record deal.

“We really started to feel that it was going to be a failure, not for us, but just in general,” Mars recalled.

But then Phoenix made “1901,” a song from the album, available for free via the Internet.

“Suddenly, overnight, people, mostly in the U.S., but other countries, too, they really liked that song,” Mars said. “That was the starting point.”

Things happened quickly. When Phoenix performed “1901” and “Lisztomania” on Saturday Night Live, a live telecast seen by millions, it was the first time they’d ever performed either song for an audience.

“Playing in front of that many people, and not having played those songs before, was very intense,” Mars said. “We felt like we were on the tightrope without safety nets. That’s something we like, this feeling of being close to success or failure.”

Creating the follow-up to Wolfgang Amadeus Phoenix was another tightrope experience.

“That’s part of the reason why this album is called Bankrupt!” Mars explained. “We got addicted to that feeling of being always on a tightrope. Especially for live performances.

“Performances need to be uncomfortable. It’s the opposite of what you do at the studio. In the studio, the album is going to last, so it needs to be a quest for perfection. Live, you’re looking for imperfection, not necessarily elegance.”

Phoenix returned to the scene of one of its triumphs, the Saturday Night Live studio, April 6, to perform two songs from Bankrupt!, an album Mars describes as a bit more aggressive, even hostile, than its predecessor.

“The sounds are big and very layered,” Mars said. “It’s not as easy to listen to as the previous one. But I think if people give it more time, the reward will be there toward the end.”

Although SNL musical guests are required to be on theset for just one rehearsal, Mars said, “even if you don’t go to the studio every day, you feel that pressure every day, for sure. That’s why, at the end of the show, when everybody’s hugging and saying goodbye, it’s real emotions. No one’s faking it, because the pressure is so high that everybody’s relieved. It’s one of the most exciting things I’ve every done, and you feel that everybody working on that show is the best of the best.”

Mars is thrilled to be playing another show in New Orleans, a city where his father-in-law, film director Francis Ford Coppola, has a home. Phoenix has a headlining spot Saturday at the New Orleans Jazz and Heritage Festival. The group’s previous two New Orleans engagements included an appearance at Tipitina’s.

“The sadness of being on tour sometimes is that all venues look alike these days,” Mars said. “But Tipitina’s is the opposite of this. When you’re on stage or backstage, definitely you feel like where you are and when you are.”

Mars also finds New Orleans, a U.S. city whose multicultural history includes much French heritage, both familiar and exotic.

“You do feel the heritage, the similarity, and at the same time it’s totally different. To me, it’s like time traveling. All those French names, they come from a different era. They are very charming to us in the band and, I think, to most French people. It’s the same in Quebec. You feel you’ve traveled to a different century.”