Patrice Couvegnes, a French national, was dismissed by the bank, the fifth largest by assets in the kingdom, in November in coordination with the central bank and other regulatory bodies after six years at the lender.
The central bank said at the time that BSF, 16.2 percent owned by Prince Alwaleed bin Talal's Kingdom Holding, might be fined over irregularities in an employee incentive programme, and had committed violations related to governance and supervisory regulations. BSF accepted that there had been irregularities in the bonus scheme that led to such violations.
Couvegnes was placed under a travel ban as a result of the investigation, the sources said.
Couvegnes could not be reached for comment. The central bank and Banque Saudi Fransi did not respond to requests for comment.
His exit followed that of two other executives, Mohamad Abdulhadi, senior executive director, and Abdulrahman Mutabagani, head of business banking, in October.
A bank spokesman said at the time that Abdulhadi had retired, but the sources told Reuters that both executives' departures, as well as that of Couvegnes, were linked to the investigation into the staff incentive scheme.
Abdulhadi and Mutabagani could not be reached for comment.
BSF first disclosed it had discovered wrongdoing in October when it said its board had appointed an independent team to investigate violations of the scheme dating back years.
Two months later, the bank said it was coordinating with authorities to recover funds related to the scheme and hold culprits to account. Reuters was unable to verify whether the investigation was still continuing.
Since taking office last year, Crown Prince Mohammed bin Salman has pushed to clamp down on corruption.
In November, hundreds of officials and business leaders were detained on his orders, on suspicion of making unfair financial gains. Most have been released after reaching settlements with the government.
Before joining BSF, Couvegnes worked at Credit Agricole in Singapore, South Korea, Japan and Hong Kong, according to his website.
After selling roughly half its stake in BSF to Kingdom Holding last year, Credit Agricole holds about 15 percent in BSF, according to Thomson Reuters data.
(Additional reporting by Stephen Kalin in Riyadh; Editing by Ghaida Ghantous and Kevin Liffey)
By Tom Arnold