Activists from the yellow vest movement, which started with protests over fuel tax increases, recommended the massive cash withdrawals on social media. One protester, Maxime Nicolle called it the "tax collector's referendum."
"We are going to get our bread back ... You're making money with our dough, and we're fed up," Nicolle said in a video message.
The movement's adherents said they hoped the banking action will force the French government to heed their demands, especially giving citizens the right to propose and vote on new laws.
Meanwhile, Prime Minister Edouard Philippe gave details Wednesday of a "big debate" the government plans to start next week in all the regions of France.
"We want it to be rich, impartial and fruitful," Philippe said.