The main CAC 40 index was down to 2,847.64 points, and banks were hard hit by concern that Moody's credit rating agency might downgrade their ratings because of the amount of Greek debt bonds they hold, traders said.

The CAC 40 already fell 3.60 percent on Friday and was dragged down further on Monday with BNP Paribas losing 11.31 percent, Credit Agricole 10.35 percent and Societe Generale 9.46 percent.

Moody's Investors Service is to issue a report mid-September on a possible downgrade of the banks' ratings.

"Fears that Moody's will downgrade French banks appear to have been reinforced. A decision could be taken in the coming days," analysts from Credit Mutuel-CIC said.

Markets also appear worried about the two Greek rescue schemes, fearing the country might not be able to respect its undertakings including budgetary austerity measures, raising the spectre of a default and sharp worsening of the eurozone crisis.

Markets are also concerned about slowing economic growth in the United States and in Europe and the fact that finance ministers and central bank governors from the Group of Seven wealthy nations did not come up with concrete measures while meeting over the weekend.