Avon's Parisian office says only current orders will be guaranteed and it is unsure if its self-employed representatives will be able to get supplies after the end of October.
Avon has been in France for almost 50 years.
It employs about 120 staff in Paris, supporting 11,000 representatives who visit customers in their own homes.
Angry workers in France have accused Avon of keeping them in the dark for months and not acting in line with Avon's publically stated values of being a socially responsible company that upholds values of trust, respect and integrity and a culture of "open and candid communication".
Estelle Croissant, an Avon employee responsible for supporting the direct selling representatives, told the BBC that a workers' council representing Avon staff in France was challenging the company for not following the correct redundancy process.
"They have not respected all the processes according to their own rules and values," she said.
"We now know an administrator has been in place since May this year, but no scheme to assist the workers is yet in place. We just feel abandoned.
"We knew that the business was not good, but we have all been very committed and worked relentlessly over many months to help the company to try and become profitable."
Further meetings are taking place between workers' representatives and the management.
Avon is one of the world's largest beauty companies and sells most of its products through direct selling by self-employed representatives who visit customers in their homes.
The US parent company has been through a string of reorganisations and management changes.
Two years ago, it turned down a takeover offer from rival cosmetic company Coty.
Asked by the BBC about events at its French subsidiary, a spokesman for the parent company refused to make any comment or even confirm the closure was taking place.
The French operations of the US cosmetics giant Avon Products are to be closed by the end of the month.