Update (11:40 a.m., EDT): Two hours into the trading day, the Dow has given back its gains from late Tuesday, shedding 430 points. Financial stocks led the decline, CNN reported, with fears of a downgrade of French markets stoking a massive slide in Paris, the echoes of which were felt here.

On Wednesday, shares of French bank Societe Generale, or SocGen, tumbled almost 20% on the Paris stock exchange amid speculation that France, Europe's second largest economy after Germany, may be first to face a rating cut.

Even though the major rating agencies have reiterated France's AAA rating, "there's growing concern that France could get downgraded," said Tom Schrader, managing director at Stifel Nicolaus. "There's fear that S&P might do something stupid."

Financial stocks led the sell-off in U.S markets, as investors worried that problems in the European banking sector could spillover into the U.S. banks.

Update (10:30 a.m., EDT): All the markets have fallen more than 3 percent at the end of the first hour of trading on Wednesday. The Dow was at 10,847.24, a 3.49 percent fall; the Nasdaq at 2,403.35, a 3.19 percent fall; and the S&P 500 at 1,126.44, a 3.93 percent fall.

Original: U.S. markets opened with sharp drops across the board on Wednesday, the Dow Jones Industrial Average recording a 1.9 percent drop from Tuesday's close, the Nasdaq 2.9 percent down, and the S&P 500 2.6 percent down. The falls follow a closing rally that ended a wild day of trading on Tuesday with massive swings in each direction.