European markets have rebounded in early trade after Asian markets steadied overnight.In London, the FTSE 100 index was up by 1.85%, Germany's Dax index was 2.2% higher and the Cac 40 in France rose 2.1%.
French banking shares were among the biggest gainers, with Societe Generale shares up 6%.
Fears about the financial stability of France and its banks were a key trigger for Wednesday's steep falls.
Rumours had swept the market that France was about to lose its AAA credit rating, and that Societe Generale was in line for a government bailout.
Denials came from both the French Treasury and Societe Generale, whose chief executive, Frederic Oudea, said the rumours were "absolutely rubbish" in an interview with CNBC television after the market closed.
Mr Oudea also spoke to France Info radio. "People are scared," he said, "so the tiniest information touches off irrational fears. To our clients, we have to tell them that these rumours are baseless and that they can have confidence in Societe Generale."
Earlier on Thursday, Asian shares were mixed, with fears about the European debt crisis still preying on investors' minds.Asian stocks pulled back from initial steep falls, with Japan's Nikkei 225 index recovering from an opening fall of 1.8% to close 0.63% lower.
Hong Kong's Hang Seng was down 0.6% - again after an earlier, larger fall.
South Korea's Kospi was up 0.62%, after earlier dropping by nearly 4%. Australia's ASX index also recouped earlier losses.
On Wall Street on Wednesday, the Dow Jones Industrial Average lost 520.29 points, or 4.6%, to close at 10,719.48. The index has now risen or fallen by more than 400 points for five trading sessions in a row.