Posing as bank employees working on IT upgrades, fraudsters contacted the unnamed France-registered company to ask for bank details and remote connection to the company bank account.
After the details were provided, a total of €642,735 disappeared from the company's account overnight, police spokesman Toms Sadovskis said.
The French company contacted both French police and the Economic Crime department of the Latvian State Police in mid-January, who quickly uncovered the scam.
The Delfi news portal has named the Latvian bank used to receive the money as Rietumu bank, but both bank and police spokespersons have refused to confirm or deny the information.
"The investigation continues and will take as long as it takes," Sadovskis told LSM.
"There is a possibility Latvian citizens were involved, so we are trying to discover the identities of all those involved."