Finance minister Michel Sapin said that new measures will be brought into force next year, Le Monde reported.
The majority of these measures had already been proposed after the Charlie Hebdo attack in Paris in January and are now being reinforced, said data protection expert Annabelle Richard of Pinsent Masons, the law firm behind Out-Law.com.
The new measures include giving Tracfin, the anti-money laundering arm of the finance ministry, access to the financial information of anyone listed on a database of people 'wanted' by the police. This includes a list called 'Fiches S', of people who have committed no crime but are simply under suspicion, said Richard.
"There is a great deal of debate about this in France at the moment. This is not a country that easily allows access to citizen's personal data," Richard said.
"The same arguments were made after the Charlie Hebdo attacks, and now both sides are saying that the latest attacks prove they were right. Those who say we need more powers say that this shows they were right, and the government should have been braver. Others say that brutally intruding on privacy has not worked," she said.
The proposed changes would not impose a great deal of change on how banks currently operate, Richard said. Tracfin already imposes a requirement on many professionals, including bankers and lawyers, to report on any suspicious activity by clients, and the scope of this is being widened notably to allow security services to request data on these individuals, she said.
Sapin also announced an initiative to improve supervision of prepaid bank cards, which he said were used by terrorists in preparation for the recent attacks in Paris. These cards work like standard bank cards but are bought 'pre-loaded' with money. Sapin proposed a tightening of the rules on how these are sold and tracked. This, too, was first proposed after the Charlie Hebdo attacks, said Richard.
There have been unconfirmed reports that Sapin will announce further measures next week, Richard said.
Richard said that the latest terrorist attacks may cause changes to be made to the draft Lemaire law for a digital republic. This law is under development and is due to be presented to parliament in January, she said.