The Journal du Dimanche (JDD) Sunday newspaper said the state had made the offer during a September 11th meeting with top officials from five banks -- BNP Paribas, Societe Generale, Credit Agricole, BPCE and Credit Mutuel.
The weekly said the plan was rejected by Societe Generale.
Issuing what it called a "formal denial," the finance ministry said the government had held talks with leading banks on their state of health but denied the bailout offer.
All the concerned banks declined comment on the JDD report, which cited sources in the Elysee presidential palace and in banking circles.
According to JDD, the plan was drawn up to bail out Societe Generale, which was badly hit by the debt crisis, but its boss Frederic Oudea -- who also heads the French Banking Federation -- rejected it as it did not extend to all affected banks and he did not want his bank to be "stigmatised."
Central bank governor Christian Noyer also rejected the report in an interview to JDD, saying there was no plan and that "French banks have a sufficient capital base compared to other European banks and they are making profits."