BNP PARIBAS Mortgage financing vehicle Caisse de Refinancement de l'Habitat (CRH) was the only one of 13 French banks to fail the tests with an aggregated capital shortfall of 129.37 million euros ($164 million).
CRH has already raised 250 million euros of capital since the end-2013 cut-off date for the tests.
CRH issues covered bonds to raise funding on behalf of its shareholders - French banks, from whom it receives promissory notes, backed by residential mortgages.
French banks have sold assets, pulled out of markets such as Greece and raised funds that could qualify for common equity tier one (CET1) capital to meet tougher post-crisis regulations and cope with weak economic conditions.
"The results for French banks confirm the quality of their assets and their capacity to withstand severe shocks," the Bank of France said in a statement.
Taking into account the ECB review of banks' assets and stress testing their accounts under adverse conditions, French banks were estimated to have an aggregate CET1 capital ratio of 9 percent at the end of 2016, the central bank said.
(Reporting by Leigh Thomas, writing by Maya Nikolaeva, editing by Mike Peacock)
