Cornet, who was cleared of an anti-doping violation on Tuesday after a charge against her for missing three out-of-competition drug tests was dismissed, picked up the injury last week in Madrid, where she was beaten in the first round by Elina Svitolina.
"I am very disappointed that I cannot take part in the Strasbourg tournament but unfortunately I have not fully recovered from an adductor muscle injury," the world number 32 said on Twitter on Thursday.
"I am going to do everything to be ready for the French Open."
Cornet, who won the Strasbourg tournament in 2013, reached the last 16 at Roland Garros last year.
The French Open runs from May 27-June 10.
(Reporting by Julien Pretot; Editing by Toby Davis)
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