"The experience of François Villeroy de Galhau no doubt offers a great expertise in the banking sector (but) it exposes him to a serious problem of conflict of interest and undermines its independence," they warned.
"Given the stakes of power and money in that vehicle, the banking sector is particularly conducive to conflicts of interest. It is totally unrealistic to say we can have served the industry bank and then, some months later, in ensuring control impartially and independently," the economists said.
French President Francois Hollande appointed Villeroy de Galhau to succeed current head Christian Noyer from October 31. The position has yet to be approved by the finance committee of the National Assembly and the Senate.
The economists asked for them not to approve it, saying Villeroy de Galhau's past employment should disqualify him from serving in an institution in which he both supervises the French banking sector in coordination with the Central Bank European (ECB) and applies the euro zone's monetary policy in France, the economists said.
"We appeal to your responsibility, your commitment to serve the public good, and your democratic sense."
They also swiped at Hollande's choice: "And it's not as if the president had no choice. It was quite possible to promote, within the Bank of France, an internal candidate less exposed to the risk of conflict of interest and providing the best guarantees of competence and experience."
It's not the first time that a former banker has taken a central bank position, but then some might say a career in the banking sector was a prerequisite for running a central bank.
Mario Draghi, the current head of the ECB, was a vice chairman and managing director of Goldman Sachs International from 2002 to 2005. He then became the governor of the Bank of Italy before his appointment at the ECB in 2011.
Bank of England Governor Mark Carney, a Canadian, also spent thirteen years at Goldman Sachs offices around the world.
- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt. Follow us on Twitter: @CNBCWorld