France's top banks are bracing themselves for a likely credit rating downgrade from Moody's, sources close to the situation said on Saturday, further complicating their efforts to assure investors they are riding out the tensions in funding markets.

Several sources said on Saturday that BNP Paribas , Societe Generale and Credit Agricole were expecting an imminent decision from the ratings agency, which first put them under review for possible downgrade on June 15.

Moody's at the time had cited French banks' exposure to Greece's debt-stricken economy as the reason behind the review, which was due to last three months. Outside commentators said the ratings were ripe for a downgrade because of rising borrowing costs in the face of sovereign debt turmoil.

The decision is imminent, one Paris-based source said. It will probably be a downgrade but it's not certain yet.

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.

The three French banks and Moody's declined to comment for this story. The agency said in June it was considering cutting BNP and Credit Agricole by one notch and SocGen by up to two notches because of the level of state aid it received in the past.

Moody's long-term senior debt ratings for BNP, SocGen and Credit Agricole are respectively Aa2, Aa2 and Aa1, all assigning high grade creditworthiness.

A downgrade, though well-flagged, would be another reminder of deteriorating market sentiment as investors discount economic slowdown in Europe, tougher capital requirements on banks and the unfolding drama in Greece and the euro area.

Sovereign debt turmoil has crushed European banks' share prices since the start of the summer and pushed up their cost of borrowing, especially from U.S. dollar money markets.

French banks, seen as particularly reliant on short-term funding, have been among the hardest hit. SocGen shares are down 57 percent since the end of June and are flirting with levels not seen since March 2009, when Europe was in recession.

SocGen, Credit Agricole and larger arch-rival BNP -- which together held around 6 billion euros ($8 billion) of Greek sovereign debt at end-March -- recently sought to reassure investors on their funding positions by giving extra disclosures on liquidity, but that has failed to stem the sell-off.

Some say the only way out is for Europe to recapitalize its battered banking sector to better absorb sovereign debt losses and to cope with tougher capital requirements. IMF chief Christine Lagarde has been a vocal proponent of such a measure.

(Additional reporting by Matthieu Protard; Editing by Ruth Pitchford)