Speaking at a hearing organised by the Committee of European Banking Supervisors (CEBS) in London, Jerome Brunel of Credit Agricole said he was "very frightened" by the plan to clamp down on bonus payments, Reuters reports.
His concerns were echoed by Guylaine Dyevre of BNP Paribas, with both executives claiming the rules would harm the competitiveness of European institutions.
Many banks are worried they will lose top staff to rivals in Asia and the US if the bonus curbs are not watered down.
"Once these rules are known and understood, it would be extremely difficult to keep our good people or recruit them," Mr Brunel commented.
Mr Dyevre suggested European banks should instead work to the principles set out by the Financial Stability Board, which are less severe.
The CEBS has said bonuses will be capped based on earnings, with only a portion received upfront and the rest deferred over three to five years.
By Tony Aynsley