Cannes this year has become a platform for stars to rail against Hollywood sexism.
"The Beguiled", which drew warm applause, marks the third outing at the world's biggest film festival for Oscar-winner Sofia Coppola, one of three female directors vying for the Palme d'Or top prize this year.
"We as women have to support female directors, that's just a given now," Kidman said, citing statistics that just over four percent of major US movies last year were made by women.
"Hopefully that will change over time but everyone says, 'Oh, it's so different now.' It isn't -- listen to that."
Cannes this year has become a platform for stars to rail against Hollywood sexism, with Salma Hayek accusing the system of treating actresses like disposable "monkeys".
Kidman plays the headmistress of a Southern girls' boarding school during the US Civil War who takes in a wounded Yankee soldier (Farrell).
The handsome corporal's presence wreaks havoc in the all-female environment, stoking desires and rivalries that explode in a violent climax.
Farrell, who also stars with Kidman in the Cannes contender "The Killing of a Sacred Deer", joked he was the "token male" on Coppola's set.
"I have a penis. Treachery and hilarity ensues," he quipped in summing up the movie.
Farrell admitted it was only his second time working with a woman director but said he aimed to pursue more female-led projects.
"I've been doing this 20 years and... I think this was my favourite experience, my favourite shoot," the Irish actor said.
"I grew up with three very strong and very brilliant, kind and smart women in my life -- my mother and my two sisters. So to be surrounded by all of these incredible women who are amazingly talented and decent and creative and insightful and curious was just a treat for me."
He praised Coppola as "incredibly smart and elegant".
"She has a gentility to her which is not to say that she hasn't got a beast of an engine inside, an incredible creative engine."
Coppola said she set out to retell the story behind the 1971 Clint Eastwood movie of the same name, but from the women's perspective.
"At the core of it there's the power struggles between the male and female which I think are relevant but hopefully in an entertaining and juicy story," she said.
The film's marketing team has playfully embraced its feminist message, using the hashtag #VengefulBitches -- one of Farrell's character's most memorable lines -- on Twitter and YouTube.
Coppola said she had long hoped to work with Kidman, who she knew "would bring her little bit of twisted humour to the role."
And she picked Farrell, known for his bad-boy antics off-screen, because he was "connected to his dark side, which the character had to have".
"We had to find a man who could handle all these women and I wanted him to be a contrast to them -- very masculine and dark and he's an exotic enemy soldier," he said.
"He comes into this feminine world and he's dark and dirty and hairy."
The picture also reunites Coppola with Kirsten Dunst for their third film, in which the US actress plays a teacher who falls hard for Farrell's soldier.
"I would do anything with Sofia," she said. "If she gave me the phone book I would do it."
Coppola first came to Cannes as a child with her father, two-time Palme d'Or winner Francis Ford Coppola.
Her last entry in the main competition at the festival, 2006's "Marie Antoinette", was loudly booed and drew mixed reviews.
This time critics called "The Beguiled" the most likely commercial hit of the 19 movies in the running for the Palme d'Or.