The 36-year-old was taken to the Clinique Monceau in Paris late on Wednesday and was operated on by brain specialist Stephanie Delajoux.
She is still in a coma, but is out of danger. Delajoux says, "The operation went well and she is not at risk anymore."
Gainsbourg--who was photographed at the Venice Film Festival earlier this week--is expected to be kept in the hospital's intensive care unit for several days.
The actress is married to actor/director Yvan Attal and they have two children together.
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