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.

Winners of the cup competition earn a place in the Europa League.
Four-time cup winners Forest have failed to progress past the third round for the past 11 seasons and start their campaign at Doncaster on Tuesday.
"It's very important because it is the only way to go into the Europa League," Montanier told BBC Radio Nottingham.
"I know it's difficult because there are a lot of teams from the Premier League and Championship. It will be a very important game."
Forest, two-time European Cup winners under Brian Clough in 1979 and 1980, who also guided the club to its four League Cup titles, last featured in European competition in the 1995-96 season, reaching the Uefa Cup quarter-finals.
The Reds, who last won the League Cup in 1990 and featured in the final in 1992, were knocked out of the competition by League One side Walsall 12 months ago.
Their trip to face League Two side Doncaster comes three days after Montanier oversaw Forest's Championship season opening victory against Burton Albion, in what was his first competitive match in English football.
Former Rennes boss Montanier also confirmed that the injury to goalkeeper Dorus de Vries, suffered in the 4-3 victory over Burton on Saturday, is not as bad as first feared.
"It will be a few weeks, but not serious," Montanier said.
The French operations of the US cosmetics giant Avon Products are to be closed by the end of the month.
[NEXT_CONCEPT]
Nottingham Forest manager Philippe Montanier says he wants to guide the Championship side into Europe next season as EFL Cup holders.