The only thing that stopped the Venice press conference for Thursday competition player “Killer Joe” from turning into a William Friedkin standup somedy show was that the vet director was sitting down.

Set in Texas, and produced by Voltage Pics and Ana Media Prod., “Joe” has Matthew McConaughey playing an upright Dallas detective with a side business as a hitman.

He’s hired by a feckless drug dealer Chris (Emile Hirsh) to kill his mother for her $50,000 insurance policy, which will be inherited by his sister (Juno Temple). Dad (Thomas Haden Church) — a non-stop beer-drinking couch potato — wants in and, since neither father nor son has a dime, he offers his daughter’s virginity to the killer for deferring the fee.

But the cop and daughter fall in love.

It’s a white-trash black comedy, propelled by an increasingly convulted plot.

But what’s it really about, an Italian journo asked the helmer of such landmark ’70s pics as “The French Connection” and “The Exorcist,” who has more recently turned to directing opera and television.

“To me this is a twisted love story, like Cinderella,” Friedkin began. “Cinderella was always looking for Prince Charming. This story she finds Prince Charming. But he happens to be a hired killer!

“All women are looking in some ways for a Prince and Princess Charming and often get a hired killer. This is true. I’ve been married four times!,” he said to laughter and applause.

“It’s not something I’m proud of. I was looking for Cinderella and instead I’ve found hired killers,” he quipped, referring to the plot of “Killer Joe.”

Friedkin made an exception for his second wife, Jeanne Moreau, “a wonderful woman and actress. What the hell she was doing with me I have no idea.” Of his current wife, Sherry Lansing, Friedkin added: “I finally found my Cinderella. I got it right this time.”

Pulitzer Prize-winning playwright Tracy Letts, who adapted “Joe” from his own 1998 screenplay, said if one thing defined Friedkin’s work it’s “obsession.”

Voltage Pictures’ Nicolas Chartier, producer of “The Hurt Locker,” told Variety “Killer Joe” had not been seen by distributors, even in footage, before its Lido world premiere.

All major territories, including the U.S., are available. “Killer Joe” has its North American premiere Sunday at the Toronto Festival.

Friedkin said his next gig is directing the opera “The Makropoulos Case” in Florence in October. It will be conducted by Zubin Mehta.