The French market regulator has warned it will investigate and punish what it called the spreading of unfounded rumours which have been blamed by some for big swings in the value of French bank shares.
Bank stock prices in France plunged and then rallied in trading on Thursday after big losses earlier this week.
Societe Generale called on France's financial watchdog, the AMF, to investigate the source of rumours about its financial health which it said were completely without foundation.
SocGen chief executive Frederic Oudea said the bank had not experienced any losses in particular and that it had come under "a series of attacks" in the stock market.
The AMF issued a statement to warn against spreading unfounded rumours.
Shares in Societe Generale fell as much as 9% on Thursday, though ended the day up 3.7%.The share price had dropped 15% the day before.
Bank of France Governor Christian Noyer said on Thursday that French banks were solid, and that would not be affected by recent market turmoil.
The French banks have an unusually high exposure to some of the European countries whose debt levels are starting to look unmanageable.
Emergency overnight borrowing from the European Central Bank (ECB) surged, with banks taking over 4 billion euros of overnight funds, the highest since mid-May.
Banking sources told Reuters that one Asian bank has cut credit lines to major French lenders while five other banks in Asia are reviewing their arrangements.