Paris councillors are due to decide on the future of a business where clients are charged €89 ($109; £78) to spend an hour with a silicone sex doll, local media report.
Communist councillors and feminist groups have been calling for the closure of Xdolls.
Currently, Xdolls is registered as a games centre, but opponents argue it is effectively a brothel.
Owning or operating a brothel is illegal in France.
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Xdolls is located in an anonymous-looking flat in the French capital and opened last month.
Clients are mainly men, though some couples also visit, owner Joachim Lousquy, who formerly managed e-cigarette shops, told Le Parisien newspaper.
Xdolls has three rooms, each containing a silicone sex doll measuring about 1m45 (4ft 7in) and worth several thousand euros.
Customers make their booking and payment online, and the exact address is kept secret. Not even the neighbours are aware of the nature of the business, Mr Lousquy says.
'Place of prostitution'
But its critics want to see it shut. Nicolas Bonnet Oulaldj, a communist councillor, is taking the matter before the Council of Paris - the deliberative body responsible for governing the city - which is meeting this week.
"Xdolls conveys a degrading image of the woman," he is quoted as saying in Le Parisien.
He and his fellow councillors are calling for a ban on Xdolls, saying it operates like a brothel.
Mr Lousquy says the dolls are sex toys and that he does not see them as degrading to women.
Lorraine Questiaux, lawyer and spokesperson for a Paris feminist association, says "that in France, every year, there are 86,000 women raped".
"Xdolls is not a sex shop. It's a place that generates money and where you rape a woman," Ms Questiaux, who also wants the centre closed, adds.