Cabrera flew home to Argentina after becoming the country's first major winner in 40 years, holding off Tiger Woods and Jim Furyk by a stroke at Oakmont on Sunday.
Cabrera gave no reason for his decision not to play at Le Golf National near Versailles when the French Open begins on Thursday, the European Tour said Friday.
Cabrera has indicated he will return to the European Tour for the Scottish Open in the week before the British Open at Carnoustie.
Darren Clarke and Ian Woosnam also have pulled out of the French Open.
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