Societe Generale's board of directors have backed the bank's chief Daniel Bouton, who had been under pressure to resign over a trading scandal.
Mr Bouton will now step up efforts to restore confidence in the bank
The bank blames junior trader Jerome Kerviel for a 4.9bn-euro ($7bn; £3.7bn) loss, though he has reportedly said it knew the risks he was taking.
Mr Kerviel was in profit as recently as early this year, the BBC has learnt.
The bank's board has said it will create an independent committee to investigate the losses.
The committee, which will be chaired by former PSA Peugeot Citroen chief Jean-Martin Folz, will be given extensive powers, the bank said in a statement.
It will work in collaboration with accountants PricewaterhouseCoopers to "ensure that the causes and sizes of the trading losses announced by the bank have been completely identified".
Mr Bouton will now remain at the helm of the bank and faces the tough task of rebuilding its balance sheet and image.
SOCIETE GENERALE IN FIGURES
Founded in 1864
467bn euros in assets under management (as of June 2007)
22.5 million customers worldwide
120,000 employees in 77 countries
Despite intense political pressure to leave, analysts say the firm is keen to show a united front to fight off a possible takeover approach - a position backed by French unions who fear that jobs could be cut if Societe Generale was bought and split up.
"We will oppose any dismantling or takeover attempt of Societe Generale," said Michel Marchet from the CGT union.
On Tuesday, French Prime Minister Francois Fillon said that the government would defend the bank against hostile bids, but the European Union has warned France against adopting a protectionist stance.
The firm's fragile position has already been exploited by rivals trying to poach its top staff and analysts say that its reputation as a high calibre employer is on the brink.
"Societe Generale is prey; nothing will be as it was," said Marc Pagezy, president of Paris-based recruitment firm Eurosearch & Associes.
Mr Kerviel will not be investigated for fraud
Pressure on the bank has been exacerbated by a group representing employee shareholders taking legal action Societe Generale over its handling of the trading scandal.
The association's members together own around 10% of Societe General capital, forming the bank's biggest shareholder.
The group's head Patrice Leclerc said: "We are filing suit because we want to be kept informed of the affair's progress."
Other lawsuits have been filed against the bank relating to alleged insider trading linked to share sales by Societe Generale board member Robert Day two weeks before the scandal emerged. Societe Generale has denied that there was any wrongdoing.
Mr Kerviel, 31, is being investigated for breach of trust, falsifying documents and breaching computer security - but not the more serious charge of fraud.
Societe Generale says Mr Kerviel had an unauthorised position, or a bet, worth about 50bn euros on the future direction of European shares.
To avoid that potentially catastrophic loss, the bank had to unwind Mr Kerviel's trades, but that still cost it 4.9bn euros.
Societe Generale said Mr Kerviel's experience in administrating trades enabled him to bypass strict risk controls. It said he invented deals that, on paper, balanced out his bets.
But in testimony published in the French daily Le Monde, Mr Kerviel said he "did not believe" the bank's senior management would have been unaware of the risky bets he was taking, which dated back to 2005.
"It's impossible to generate such large profits with small positions, which leads me to say that when I'm in the black, my superiors close their eyes about the methods and volumes committed," he was reported as saying.
The bank's lawyers have accused Mr Kerviel of lying.
On Tuesday, France's financial market regulator said it had opened an investigation into Societe Generale but did not provide further details.