This made her more than 10 times over the legal limit in France of 0.5 grams.
Her level of intoxication was a record for the Auvergne region where she was caught.
"Alerted by the zigzags she was making in her vehicle on the road, the police intervened although they didn't ask her to take an alcohol test" reported local newspaper La Montagne.
It was at the hospital in nearby Aurillac that the woman's blood alcohol level was found to be the highest ever recorded in the area.
It is estimated that three small glasses of wine would be enough for a 75-kilogram man to pass the 0.5 grams limit. It is not known what the woman had drunk.
The record for drunk driving in France was set in 2005 when a man in Polliat, in the east of the country, was found with a blood alcohol level of 9.75 grams.
Although public drunkenness is relatively rare in France, the country has a less than stellar record when it comes to drink driving.
A 2009 report commissioned by the European Commission found that the French were the most likely of all Europeans, with the exception of Cyprus, to drive after drinking even a small amount of alcohol.
47 percent of the French people questioned said they would never drive after drinking. This compared with 66 percent of Germans, 75 percent of those in the UK and 90 percent of Swedes.
France’s road safety association, Association Prévention Routière, reports that alcohol is the biggest factor in deaths on the road with 28.5 percent of deaths involving a car driven by someone with an excessive blood alcohol level.
A crackdown on drink driving and other road safety measures has helped to cut the number of deaths on the road by half over the last ten years.