Société Générale, France's second-biggest bank, lost more than a fifth of its stock exchange value at one point on Wednesday afternoon following rumours that the bank was in serious financial difficulties and had held an emergency meeting with France's president, Nicolas Sarkozy.

Shares in Société Générale fell by as much as 23% to their lowest point for more than two-and-a-half years at one point. They recovered later to close down 14.7% at €22.18.

The sudden fall in the shares, which wiped almost €3bn (£2.6bn) off the company's market value, raised fears that the 147-year-old bank might be on the brink of collapse. A Société Générale spokesman said the bank "categorically denies all market rumours", but he refused to comment more specifically.

The bank did say that it was not present at emergency government talks today organised to discuss France's growing debt burden and suggestions that the country could be on the brink of losing its AAA credit rating.

Sarkozy returned from holiday to chair the two-hour meeting of France's financial ministers and central bankers at the Elysée palace. After the meeting, he sought to reassure the country that France's plan to cut its budget deficit from 7% of GDP in 2010 to 3% in 2012 would be enough to ensure a stable economic future.

France's finance minister, François Baroin, said: "We will take the necessary measures to reach these goals." His colleague, budget minister Valerie Pécresse, later announced a tightening of some tax breaks in France, without giving any details. "We will end tax breaks… because we will not be increasing taxes," she said. "These exonerations from taxes, which are justified in some cases, are in some cases very inefficient."

Until now, Sarkozy had refused to return from holidaying in the south of France. Only 24 hours before his return, Sarkozy's advisers were telling journalists: "If the president came back to Paris it would dramatise the situation for nothing", adding that it was important the French leader was not seen to "overreact" to the crisis.

French banks collectively hold more than €40bn of Greek debt, which is almost four times more than any other country. Last week SocGen revealed that its profit for the second quarter fell to €747m, down 31% from a year ago, after a €395m writedown on its Greek debt holdings. SocGen has about €2.65bn worth of Greek sovereign bonds and warned that its 2012 profit target would be "difficult to achieve".

Its shares have lost more than half their value since February and Wednesday's plunge dragged down the shares of other French banks, including BNP Paribas, which fell 9.5%, and Crédit Agricole, which dropped 11.8%. The contagion also spread to British banks, with Barclays shares falling 9% and RBS 7%.

Fears that France was about to be downgraded were, however, eased when a Standard & Poor's analyst said that France seemed more serious than the United States in addressing fiscal issues, and that its AAA rating was not at risk.

Nikola Swann, S&P's top analyst for the United States, also said France had better fiscal flows and lower budget deficits than the US, although indebtedness ratios are similar in both countries.

Despite S&P's intervention, investors are concerned that France could be the next country to lose its AAA rating because of its high public deficit and exposure to the Greek crisis. Analysts at Citigroup said: "We expect that France, with its high public debt and deficit, and popular resistance to cutbacks in its, even by euro area standards, extremely large welfare state, is now likely to be the G7 country at the highest risk of losing its AAA rating.

"The markets appear to share this sentiment, with French 10-year spreads over German bunds reaching 16-year highs of 90.7 basis points on Friday … levels not seen since the last of the major ERM crises in December 1994."

A spokesman for the French ministry of finance said the downgrade rumours were "totally unfounded" and that "the three agencies, Standard & Poor's, Fitch and Moody's, have confirmed that there is no risk of a downgrade".

A spokesperson for the Autorité des Marchés Financiers, the French equivalent of the Financial Services Authority, said: "As with any period of turbulence we are being vigilant. We are keeping a close watch on the markets and in particular the valuations of financial services companies."