The proposals for "new unprecedented sanctions" were addressed to the leaders of Britain, Canada, Germany, Japan and the United States, as well as European Union leaders, the French presidency said in a statement.
"As Iran speeds up its nuclear programme, refuses negotiations, and condemns its people to isolation, France is in favour of new unprecedented sanctions to convince Iran that it must negotiate," said the statement.
"For more than 10 years Iran has been pursuing an illegal nuclear programme and developing a military nuclear capacity, as shown by the International Atomic Energy Agency (IAEA)," it said.
The French announcement came hours after Britain announced it is severing links with Iranian banks because of evidence that they are involved in the development of a nuclear weapons programme.
The United States said it would follow Britain later on Monday with new restrictions on Iran, expected to target the financial, oil and petrochemical sectors.
The moves appeared to be part of coordinated efforts by Western governments to isolate Tehran, which has already been hit by four sets of UN sanctions.
The French statement stressed that "the behaviour of the Iranian regime constitutes a grave threat," it said. "In addition to the inacceptable threat of nuclear proliferation there is now the added risk of a military escalation in the region, the consequences of which will be catastrophic for Iran and for the world."
Thus France is proposing "to freeze Iran central bank assets effective immediately" and "to stop the buying of Iranian oil" in "coordination with the countries of the region."
"We demand Iran immediately suspend all its prohibited nuclear and ballistic activities" and "stop its threats to its neighbours and other countries in the region."
"If Iran wishes it, negotiations in good faith, as our countries have called for, is possible."
Some experts have cautioned that targeting the Central Bank could have a profound impact on Iran's economy and global energy prices.
Iran stayed away on Monday from a UN atomic agency forum on creating a Middle East free of nuclear weapons, with its ambassador to the Vienna-based body, Ali Asghar Soltanieh, attacking last week's report as "inappropriate."