Fillon, however, said in the interview with Les Echos business newspaper that the state would not allow any banks to fail.
"French banks are not insulated from difficulties if a large European bank collapses," he said.
"For that reason, we are assuring the French people of the state's absolute guarantee of the French banking system.
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The prime minister said "we are totally mobilised... We will not rule out any solution...
There will be no bankruptcies."
Fillon said the state could take action in the same way it did with Dexia, which became the latest European bank to require a bailout Tuesday, with Belgium, France and Luxembourg pumping 6.4 billion euros into the group.
Dexia's troubles came amid a growing storm in the global financial sector, with the US government trying to get a 700-billion-dollar rescue package passed in a bid to limit the turmoil.
"The crisis we are facing is serious because we have a financial crisis equivalent to that of 1929 that is in additio