The maximum fine the state banking commission can levy for breach of its rules is five million euros ($7.4m). Lagarde said this should be "substantially increased".
Her 11-page report, drawn up jointly with the French banking commission and the financial markets authority, the AMF, "identifies several points that may have been decisive" in the run-up to the scandal, the finance ministry said in a statement.
Lagarde's report suggested other banks could be susceptible to similar problems and urged greater controls on banks in France and worldwide.
On January 24, Societe Generale announced billion-dollar losses in the biggest rogue-trading scandal in history, for which Jerome Kerviel, a 31-year-old junior trader, has been charged.
Once the bank discovered Kerviel's positions, it unwound the deals over three days, despite a slumping market, resulting in losses of 4.8bn euros ($7.1bn).
Lagarde's report found that the bank acted "in a professional manner" when it unwound the deals and had kept the financial markets sufficiently informed.
But she also said the bank should have informed the government of the suspicious activity earlier.
Since the scandal, rumours of takeover bids have been circulating, with BNP Paribas, France's largest lender, last week saying it was considering whether to bid for the troubled bank.
BNP Paribas tried, but failed, to acquire Societe General almost 10 years ago.