The punishment was for a number of failings picked up during regular checks carried out in 2015, said the ACPR, the bank and insurance supervisory body.
Societe Generale had been slow to release information to Tracfin, the economy ministry body that tracks the movement of money that could be used to finance terrorism.
In addition, some operations which should have been brought to Tracfin's attention had not been, and these were significant lapses given the bank's size, the agency added.
In June the ACPR fined another French bank, BNP Paribas, 10 million euros for similar lapses.
The ACPR is the part of the Banque de France that is tasked with ensuring the stability of the nation's financial system.
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