By Pamela McClintock

Tue May 31, 2011 2:38am EDT

LOS ANGELES (Hollywood Reporter) – Did winning the Palme d’Or at the Cannes Film Festival do the trick for “The Tree of Life,” a new drama starring Brad Pitt and Sean Penn?

The film grossed an estimated $352,000 during its opening weekend in a total of four theaters in New York and Los Angeles. Its per-screen average of about $88,000 is a record for a film released by Fox Searchlight, surpassing the $80,000 average for “Black Swan” last year.

The critically acclaimed film’s performance was all the more impressive given its lengthy running time of 138 minutes, said Sheila DeLoach, the studio’s executive VP for distribution. And Fox Searchlight relied almost entirely on publicity to generate interest in the drama, versus an expensive media campaign.

“Winning the Palme d’Or really pushed it forward,” DeLoach said.

The last American film to walk away with the festival’s top honor was Michael Moore’s documentary “Fahrenheit 9/11″ seven years ago.

“Tree of Life” isn’t the only film feeling the Cannes glow. Woody Allen’s “Midnight in Paris,” the festival’s opening-night film, remained strong business in its second weekend.

The Sony Pictures Classics release jumped six places to No. 7 with $1.9 million from 58 theaters; its 10-day total rose to a stellar $2.8 million. Last weekend, “Midnight” scored one of the best location averages of all time — $99,834 — when opening in six theaters.

“Tree of Life” had a long and twisted journey to the big screen. The film’s producer, Bill Pohlad, originally intended to open the movie in late 2009, but notoriously perfectionist director Terrence Malick wasn’t done in time. Nor was he

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