The woman, who recently returned from a visit to Liberia, has been moved to an isolation ward in the northern Parisian hospital Bichat, according to Europe1 radio.
On Thursday doctors changed the case's classification from suspected Ebola to probable.
Blood test results were expected to confirm that it was Ebola.
The woman is not a healthworker, RMC radio reported, adding that she has just returned from a trip to Liberia.
The health ministry on Friday did not confirm or deny the reports.
"If an Ebola case were to be confirmed in France, the public would be informed immediately," an official said. "But that is not the case at the moment."
Prime Minister Manuel Valls warned the media and the authorities against causing "a movement of panic" on Friday
Concern is growing in France after a Spanish nurse was found to have been infected in Madrid and seven other Spaniards were hospitalised.
A public building in a Parisian suburb was shut off on Friday morning for 90 minutes after an African man showed Ebola-like symptoms but the incident was later found to be a false alert.
"An Ebola epidemic in Europe is highly unlikely," a spokesperson for European Health Commissioner Frédéric Vincent said on Thursday.
Scientists last weekend estimated there was a 25 per cent risk of Ebola reaching France within the next 20 days.
The UK on Friday strengthened its security measures at airports and railway stations after a British citizen displaying Ebola-like symptoms died in Macedonia.