Marie Helleux and her husband Patrick Motais came to the police station in Hoan Kiem District to get the money on Sunday, they said on Tuesday as cited by VTV24 newspaper.
They are completing the investigation into the driver's acts.
On May 12 a tour guide who had taken them around, wrote on social media that the couple had taken the taxi from Tran Nhat Duat to Cho Gao Street, a 200-meter ride, and were charged VND500,000, 20 times the normal fare.
After getting off the taxi, Motais discovered he had forgotten his wallet and passport in the car.
The driver did come back to return them but demanded another VND500,000 for doing so.
The couple paid him but took a photo of the driver's car and license plate.
They then told their guide to complain to authorities.
Helleux said: "I am very grateful to the Vietnamese police."