She was seen as one of the brightest young talents in climbing, a sport which will be introduced to the Olympics in Tokyo next year.
It is one of the disciplines when sports climbing makes its debut at next year's rescheduled Tokyo Olympics.
"This bad news has had a huge impact on her training partners, her coaches and her club, Chambéry Escalade", the FFME statement read in part.
COVID-19 cases in India cross 2.86 lakh, death toll at 8,102
Earlier on Thursday, India passed the United Kingdom in terms of coronavirus cases to become the fourth worst-hit country. Coronavirus Tally Crosses Three Lakhs In India :- The new cases of coronavirus are fastly increasing across the country.
Her body has been recovered and an investigation opened, with the exact circumstances of her death yet to be determined.
After winning youth events Douady moved on to senior competition. FFME added that "the whole federation is in mourning", including Douady's "training comrades and coaches".
She also debuted fifth in women's bouldering in Vail, Colorado at the International Federation of Sport Climbing Boulder World Cup previous year.
Her club, Chambéry Escalade, described Douady as a "beautiful person" in a statement on Facebook Monday. The climber performs on small rock formations or climbing walls and doesn't use safety equipment like ropes or harnesses.
"Luce was a very promising young athlete from the French climbing team", the statement said.