The bones came from a mummy, Philippe Charlier says
In 1867, a jar was found in a Paris pharmacy attic, along with a label claiming it held relics of Joan's body.
But new forensic tests suggest that the remains date from between the third and sixth centuries BC - hundreds of years before Joan was even born.
The study has been reported in the news pages of the Nature journal.
Forensic scientist Dr Philippe Charlier, who led the investigation, told Nature: "I'd never have thought that it could be from a mummy."
France's national heroine - canonised in 1920 - was convicted of heresy and witchcraft and burned alive in 1431, aged just 19.
The "relics" were said to have been found at the stake in the Normandy town of Rouen where Joan was burned.
In medieval Europe it was common practice to throw black cats into the pyres of supposed witches.
Recognised as genuine and sacred by the Church, the "remains" are now housed in a museum in Chinon belonging to the Archdiocese of Tours.
Dr Charlier, from the Raymond Poincare Hospital in Garches, near Paris, obtained permission to study the relics from the France's Catholic Church last year.
He used a range of scientific tests such as spectrometry, electron microscopy, and pollen analysis.
The researchers also found pollen from pine trees, probably from resin used in ancient Egyptian embalming. Pines did not grow in Normandy during the 15th Century.
Dr Charlier also recruited two smell experts, Sylvaine Delacourte and Jean-Michel Duriez, from the perfume industry.
They were independently asked to sniff the relics as well as nine other samples of bone and hair from Dr Charlier's lab without being told what they were.
Both smelled hints of "burnt plaster" and "vanilla" in the samples. The plaster smell backs up claims that Joan was burnt on a plaster stake, to make the spectacle last longer.
But a vanilla smell is inconsistent with cremation. It comes from the compound vanillin, which is released during the decomposition of a body.
Analysis of the black crust covering the rib and the cat bone showed that it was not caused by fire, but an embalming mix of wood resins, bitumen and chemicals such as malachite.
In medieval times and later, powdered mummy remains were used for medicinal purposes, "to treat stomach ailments, long or painful periods, all blood problems," Philippe Charlier told the Associated Press.
The researchers' assumption is that a 19th Century apothecary was behind the fake, and transformed the remains of an Egyptian mummy into a fake relic, Dr Charlier said.
Why it was done remains a mystery.
According to Philippe Charlier it was probably not for money: "Perhaps it was for religious reasons."Perhaps it was created to increase the importance of the process of beatification in 1909."