Deneuve is now being treated at Pitié-Salpêtrière Hospital, a facility that specializes in strokes.
The newspaper had added that she was in a "serious state" following the illness.
She was most recently featured in The Truth, which opened the Venice Film Festival, and is now working on De Son Vivant.
Catherine rose to fame in the and was known as "Ice Maiden" for her cool manner and enviable beauty.
The Hollywood Reporter has reached out to her reps.
In 1993, she was nominated for an Oscar for her tole in "Indochine".
Last year, she apologised to victims of sexual assault after signing an open letter arguing that the campaign against sexual harassment had gone too far.
Deneuve's agent, Claire Blondel, shared that the European star suffered a "no motor function deficit, and must of course take some time off".
"A source told French television network BFMTV that Catherine had recently been suffering from 'exhaustion'".
One of Catherine's most successful recent films, The Midwife, earned worldwide acclaim. She had a son, Christian Vadim, with director Roger Vadim, and a daughter, French actress Chiara Mastroianni, with actor Marcello Mastroianni, with whom she had lived.
We hope Catherine makes a quick recovery!