"It's going well. The investigation led by the experts from the financial brigade is extremely fruitful," Jean-Michel Aldebert, head of the office, said.
The bank, which suffered the largest ever losses by a bank, alleged that Kerviel was holding more than 50bn euros in deals when he was caught.
Quick action was taken to liquidate the value of the deals, limiting losses to 4.9bn euros, the bank said in a statement on Sunday.
Aldebert said Kerviel was providing "very interesting" facts and that he told investigators he was feeling fine.
Criminal complaint
Societe Generale has filed a criminal complaint against Kerviel, alleging the use of falsified documents and unauthorised computer access to cover up failed deals on share futures and hedges worth tens of billions of dollars.
But Kerviel's lawyers have hit back, accusing the bank of trying to "create a smokescreen" to cover up wider losses accumulated in the midst of the US subprime mortgage crisis.
Elisabeth Meyer and Christian Charriere-Bournazel said on Sunday that their client had "committed no dishonest act, did not siphon off a single cent, and did not profit in any way".
Kerviel had bought futures in three European indices - the Eurostoxx, the DAX in Frankfurt and the FTSE in London - gambling on the future direction of the stock market.
Barings parallel
The losses sustained by Societe Generale dwarf those of Barings Bank, a British bank which folded after Nick Leeson, lost $1.5bn in a 1995 trading scandal.
Investigators are looking to establish Kerviel's motives, how he allegedly managed to elude detection and whether he acted alone, said a source close to the case.
He joined Societe Generale's investment banking department in 2000 and moved five years later from the back offices to the front office where he began trading in futures.
Daniel Bouton, Societe Generale chairman and chief executive, described Kerviel as a "crook, fraudster and terrorist", but colleagues have portrayed him as quiet and shy.
Management scapegoat?
Kerviel's aunt suggested he is being made the scapegoat for mismanagement or other wrongdoing at the bank.
"You have to look around in his entourage, his superiors and management [to find those to blame for the losses]," Sylviane Le Goff said in an interview with RTL radio.
"Jerome is an honest and serious boy who is close to his family."
Bouton denied suggestions by analysts that the bank may have sunk losses from other bad deals into the case.
Societe Generale said it also lost 2bn euros in subprime deals.