"We will be watching over the sound functioning of the markets and in particular, the banking stocks which suffered badly (on Wednesday)," an AMF spokesman said.
Shares in French banking giant Societe Generale briefly crashed more than 20 percent on Wednesday, before recovering some lost ground, as concerns about Greek debt and that France could be next to lose its top credit rating shook the market.
Societe Generale closed down nearly 15 percent and other banks also fell sharply as the financial markets sold off heavily again.
Societe General said all the rumours swirling around the market about its financial health were completely unfounded and it demanded that the AMF investigate their origin, saying they had seriously damaged the interests of its shareholders.
The tumble came after Greece said that its exchange of bonds under its latest rescue might include instruments with a life stretching slightly beyond the target date of 2020 and that the swap procedures had not yet begun.
French banks and insurers have agreed to reschedule 15 billion euros' worth of Greek debt as part of an EU rescue package to stabilise the eurozone.
Societe Generale announced last week its second quarter net profit slumped 31 percent to 747 million euros ($1.07 billion), largely because of its exposure to debt-stricken Greece.
Britain's Mail on Sunday newspaper apologised for an article published last Sunday that suggested Societe Generale was on the "brink of disaster".
"We now accept that this was not true and we unreservedly apologise to Societe Generale for any embarrassment caused," it said in a statement.
The tumble of the bank's share price also came as President Nicolas Sarkozy broke off his summer vacation to meet with ministers to discuss France's deficit-reduction plans amid the debt crisis rattling global markets.
The government categorically denied speculation that France might be the next major country to lose its top AAA status after the United States lost the coveted credit rating last week.
The Fitch ratings agency later confirmed that France was retaining its top triple-A credit rating and said the outlook was stable.
Copyright AFP (Agence France-Presse), 2011