Stocks fell sharply on Wednesday, wiping out most of the previous session's gains, on fears of tumult in the French banking sector, which has significant exposure to shaky European debt.

U.S. financial stocks led the decline on worries that any French bank problems could spread to them. The KBW bank index slid 6 percent. Large financial institutions' shares sank, including Bank of America Corp, down 7.2 percent at $7.05.

French banks' shares tumbled in Paris trading even after a Societe Generale spokeswoman denied rumors of trouble. Societe General, where U.S. traders have focused their attention, fell 14.7 percent and BNP Paribas dropped 9.5 percent.

You've already had situations in Greece, Spain has been in there, Portugal, and now if you are talking about France, which because it's a bigger economy, it probably generates more concern on a comparison basis, said Gordon Charlop, managing director of Rosenblatt Securities in New York.

So there are investors who are a little bit more cautious about European financials and that translates into financials here.

Stocks rallied on Tuesday after the Federal Reserve promised to keep interest rates near zero for at least two more years. The S&P 500 index had its best performance in more than two years.

Investors are kind of pondering Bernanke's message and are probably looking for something more than they got. They might be selling into the meeting that he is having at Jackson Hole -- that could be part of it, too, Charlop said.

The Fed chairman is due to give his yearly speech at the Jackson Hole, Wyoming, meeting at the end of August.

The Dow Jones industrial average dropped 363.17 points, or 3.23 percent, to 10,876.60. The Standard & Poor's 500 Index lost 36.12 points, or 3.08 percent, to 1,136.41. The Nasdaq Composite Index fell 70.01 points, or 2.82 percent, to 2,412.51.

The CBOE Volatility Index shot up 19.1 percent. Earlier, the VIX had climbed slightly more than 20 percent, representing the third session in the last five that the index has jumped at least 20 percent.

Walt Disney Co was among the Dow's worst performers, tumbling 9.6 percent to $31.38 a day after the company's quarterly results failed to reassure investors that the entertainment company could do well in a weak U.S. economy.

Even after Tuesday's snap-back rally, the S&P 500 is down nearly 17 percent since its 2011 closing high set on April 29. Worries about the U.S. economy and high levels of public debt in Europe have sent stocks cascading down sharply over the last two weeks.

(Reporting by Chuck Mikolajczak; Additional reporting by Ashley Lau; Editing by Jan Paschal)