The ratings agency said it was extending its review of BNP Paribas (BNPP) (BNPP.PA), but any downgrade was unlikely to be by more than one notch.
Moody's had put the banks under review for possible downgrade on 15 June, citing their exposure to Greece's debt crisis.
Moody's at the time had cited French banks' exposure to Greece's debt-stricken economy as the reason behind the review. Outside commentators had said the ratings were ripe for a downgrade because of rising borrowing costs in the face of sovereign debt turmoil.
The agency said that during the review, Moody's concerns about the structural challenges to banks' funding and liquidity profiles increased, in light of worsening of refinancing conditions.
Moody's cut SocGen's debt and deposit ratings by one notch to Aa3 from Aa2. The outlook on the long-term debt ratings was negative. Moody's anticipated that the impact of its review on the Bank Financial Strength Rating (BFSR) would be limited to a one-notch downgrade.
For Credit Agricole, Moody's downgraded its BFSR by one notch to C from C+, and cut its long-term debt and deposit ratings by one notch to Aa2 from Aa1.
However, Moody's said it believed SocGen has a level of capital that can absorb potential losses it is likely to incur on its Greek government bonds and to remain capitalized at a level consistent with its BFSR even if the creditworthiness of Irish and Portuguese government bonds were to deteriorate further.
Moody's said that BNPP had a sufficient level of profitability and capital that it can absorb potential losses it is likely to incur over time on its Greek, Portuguese and Irish exposures.
BNPP on Wednesday announced a plan to sell 70 billion euros ($95.7 billion) of risk-weighted assets to help ease mounting investor fears about French bank leverage and funding, two days after smaller rival Societe Generale unveiled a similar plan.
France's lenders -- two of which own local banks in Greece -- have the highest overall bank exposure to Greece, according to the Bank for International Settlements. They have begun to take writedowns on their Greek sovereign debt holdings as part of a new rescue package but some say not aggressively enough.
Greece vowed on Saturday to stay the course of austerity and avoid bankruptcy as anger at the country's failure to meet fiscal targets under its EU/IMF bailout reached boiling point.