Societe Generale led European bank stocks back up Thursday, a day after rumors about its financial health prompted another bout of turmoil in the financial markets and reinforced the skepticism over Europe's ability to deal with its debt crisis.

France has become the latest to be caught in the crossfire and its government is taking pains to assure markets that it won't be the next to see its credit rating downgraded. French President Nicolas Sarkozy cut short his holiday Wednesday and ordered his ministers to come up with new budget cuts to ensure that France sticks to deficit-cutting targets.

However, his return did little to soothe investor worries about the country's rating even though all three leading credit rating agencies reaffirmed their current triple-A assessment of France.

Societe Generale, France's second biggest bank, bore the brunt of Wednesday's market skepticism as its share price became a massive victim of rumors surrounding its financial health.

In light of the turmoil, which saw the bank's share price drop nearly 15 percent Wednesday, the bank has asked the French market regulator, the AMF, to investigate the rumors that it was on the ropes because of its heavy exposure to debt from troubled eurozone economies.

Societe Generale CEO Frederic Oudea on Thursday called the rumors "totally unfounded" and "irrational." Speaking on France-Info radio, he urged calm and insisted that the bank's fundamentals are sound.

The bank's shares were momentarily suspended at market opening Thursday then rapidly regained some of the lost ground, and were trading around 7 percent higher in morning trading in Paris.

Oudea said Societe Generale had already accounted for its exposure to Greece's debts in its second quarter earnings.

"We are in an extremely nervous market, extremely volatile," he said.

Worries that France would lose its coveted triple-A credit rating sparked Wednesday's selloff, which built momentum on rumors over Societe Generale

"S&P is not going to downgrade France any time soon. Nor are Moody's or Fitch," Gary Jenkins of Evolution Securities said. "Growth will be the key to the stability of the ratings for France, U.K and the U.S. over the next 12 months."

He said there will be extra attention to France's release of second-quarter GDP figures on Friday, and warned that France could suffer if it has to spend significant new money to bail out more struggling eurozone states.

France's growth prospects are considerably better than those of Italy and Spain's, but its economic expansion is slowing and it's failed for years to reduce a deficit that stood at 7.1 percent last year. No other eurozone economy with a triple-A rating has a higher debt than France's — around 85 percent of national income.

Adding to market worries, French presidential elections scheduled for the spring of 2012 may make it difficult for the government to implement further austerity measures at a time when the economy is slowing.