The three French banks are being investigated for violating US embargoes and sanctions on countries like Cuba, Iran and Sudan and for embezzlement and money-laundering," the source told the AFP news agency.
Other big international banks were also cited in the investigation, according to the source, who refused to confirm their names or say when the probe was launched.
The US Treasury, Justice Department, Manhattan district attorney and New York Department of Financial Services are all investigating the banks.
BNP Paribas, France's largest listed bank, apparently expects a record fine to be imposed and is in talks with US authorities to settle the probe, according to the Wall Street Journal.
Last month it said it had set aside 806 million euros to cover potential penalties for transactions in countries under US sanctions.
Press reports said the investigation related to its dealings with Iran.