Cornet was no match for China's Australian Open runner-up Zheng on Court Philippe Chatrier, losing 6-2, 6-1.
She made her debut at Roland Garros as a 15-year-old in 2005 and has not missed a Grand Slam tournament since the 2006 US Open.
Cornet reached a career-high ranking of 11th in 2009 and enjoyed a surprise run to the 2022 Australian Open quarter-finals.
