Le Figaro reported that the mix-up occurred in the Bichat hospital in northern Paris in early May.
The bodies of two deceased women were placed side-by-side in the hospital mortuary.
A 92-year-old woman was placed next to that of a 71-year-old.
The body of the older lady was due to be cremated while the other was planned to be buried.
The cremation took place as planned on May 4th in Paris' Père-Lachaise crematorium and in the presence of the lady's family.
However, a few days later the undertakers received a call from the hospital to say the wrong woman had been cremated.
The mistake was the result of the two bodies being swapped around.
The deputy director of the Bichat hospital said the error was the result of a "series of unfortunate circumstances."
"The two bodies were placed next to each other. We took one out to show to the family but when it was returned it was put in the place of the other body."
The mix-up was spotted just as the coffin was being sealed for the second body.
The families have been informed and a second cremation has now been planned for May 21st.
The remains of the first woman will be returned to the family so they can be buried.
The Bichat hospital has opened an internal inquiry into the incident.