"We will cooperate fully with the judicial authorities," Shein's spokesman in France, Quentin Ruffat, told RMC radio, adding the company was prepared to share names of those who have bought such dolls.

"We will be completely transparent with the authorities. If they ask us to do so, we will comply," he said.

"We will put the necessary safeguards in place to ensure that this does not happen again," Ruffat said, adding that what has happened is "serious, unacceptable, intolerable."

The Paris prosecutors' office said it had opened investigations against Shein, and also rival online retailer AliExpress, over the sale of sex dolls.

The probes were also for distributing "messages that are violent, pornographic or improper, (and) accessible to minors", the office told AFP.

The investigations were launched after France's anti-fraud unit reported on Saturday that Shein was selling childlike sex dolls.

On Monday, Shein announced it was imposing a "total ban on sex-doll-type products" and had deleted all listings and images linked to them.

The uproar comes as Shein prepares on Wednesday to open its first physical store in the world inside the prestigious BHV Marais department store in central Paris.

Finance Minister Roland Lescure had warned he would move to ban the company from the French market if the items returned online.