Stone plays King in the story of her famous 1973 tennis match against retired former champion and male chauvinist Bobby Riggs, played by Steve Carell.
"I think the thing that was most inspiring to me...was that Billie Jean was going through so many personal trials at the time and discovering so much about herself," Stone said on the red carpet at the Toronto International Film Festival.
Along with the highly-publicized grudge match, the film also covers King's sexual exploration via a off-court relationship with a woman. She did not publicly identify as a lesbian until 1981.
"In this time period she was confused and scared and still was able to effect such massive social change," said Stone, who won an Oscar earlier this year for "La La Land".
King, who won the match, played a pivotal role in the fight for equal pay for female athletes and is considered a major influence on the women's liberation movement as a whole.
But more than 40 years later, the issue of equal pay, both in tennis and the wider working world, is still simmering.
"It's eerily relevant these days, and sadly it's, I think, more relevant than it should be at this point," Carell said ahead of the screening.
A tennis tournament executive, Raymond Moore of the BNP Paribas Open, last year said that top-level women's players rode "on the coattails of the men" and were "very, very lucky" to have equal prize money.
He stepped down from the role several months later amid heavy criticism, with tournament owner Larry Ellison citing King's "historic campaign for the equal treatment of women in tennis" when announcing the move.
The film has received early awards-season buzz since first screening at Telluride earlier this month, with Stone's performance especially well-received.
The Toronto festival is an important stop for filmmakers looking to showcase their work in the long Hollywood awards season that culminates with the Oscars on March 4.
"Battle of the Sexes" was directed by husband and wife team Valerie Faris and Jonathan Dayton, who previously worked with Carell for their 2006 film "Little Miss Sunshine". Stone and Carell had previously worked together on 2011's "Crazy, Stupid, Love".
(Reporting by Alastair Sharp and Reuters TV; Editing by Simon Cameron-Moore)
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