The Lady tells the love story between Nobel Peace Prize winner Aung San Suu Kyi and her husband Michael Aris (David Thewlis). In 1989, Suu Kyi was placed under house arrest for her activism and only was released in 2010.
The Kung Fu Panda 2 actress told Indiewire that she and Besson wanted to do a film together that was "very special".
She explained: "We've been trying to work on a project for the longest time and we've always said, 'Until we find a project that blows us away, we're not going to take time away from our family'.
"When you're such good friends, you should never do something just for the sake of doing it. It has to be very special.
"We're trying to make a movie about a woman who's under house arrest, whose husband died 11 years ago, so we knew it was going to be very difficult to get information. I needed to know, technically, legally, whether it was even possible to embark on such a dream.
"I think after he took the script and read it, he fell in love. We both knew that no matter how difficult, nothing was going to stand in our way of making this movie."
The actress revealed that she started preparing for the role four years ago, relearning how to play the piano and learning how to speak Burmese.
Yeoh, who said that she considers Suu Kyi to be an inspiration, also added that she was able to meet with the activist before her release from house arrest.
In June, Yeoh was deported from Burma over her role in The Lady.
Watch the trailer for The Lady below: