Socialist Hollande and his finance minister have spent the past week fending off accusations of a cover-up after former budget minister Jerome Cahuzac admitted lying about a secret 600,000-euro (RM2.4 million) foreign bank account and was placed under formal investigation by magistrates.
The scandal is a grave blow to Hollande, who had promised his administration would be irreproachable, and raises the pressure on the government as it struggles to reverse a rise in unemployment and meet its economic targets.
A survey by IFOP for the weekly Journal du Dimanche on Sunday showed that 60 percent of French people wanted Hollande to reshuffle his team, including 42 percent of left-wing voters.
The poll also said 55 percent of people felt Hollande's image had been tarnished at a time when approval ratings have already slumped to below 30 percent for both him and his prime minister, Jean-Marc Ayrault.
"For the French, the Cahuzac affair is not an isolated case," said IFOP's Frederic Dabi. "There is a distrust towards elected officials."
Hollande, who during his election campaign vowed his main enemy would be the world of finance, faced further scrutiny on Thursday over the business dealings of his campaign treasurer.
French media, citing leaked corporate data, reported that Jean-Jacques Augier had joint ownership of two firms registered in the Cayman Islands, a Caribbean tax haven.
Hollande has said he had no knowledge of his long-term friend's businesses, while Augier is not suspected of doing anything illegal.
The Cahuzac scandal and Hollande's low popularity have fed media speculation that the president will have to reshuffle his cabinet, with predictions ranging from the removal of Finance Minister Pierre Moscovici to replacing Ayrault.
Hollande and his ministers have so far dismissed the possibility of a quick-fire reshuffle.
"The response is not to say that everybody is rotten and we need a shake-up," Moscovici said on Europe 1 radio.
But fresh allegations on Sunday have again put the spotlight on the scandal. Swiss media said Cahuzac may have falsified a tax certificate to open an account and that the sums he wanted to transfer were between 10 million and 15 million euros rather than 600,000 euros. He has made no immediate comment about the Swiss allegations.
Moscovici, Cahuzac's direct superior, was again forced to fight suggestions that he knew about the accounts and defend the government's handling of the affair.
"I am not the minister for the Cahuzac scandal," an irritated Moscovici said. "I neither tried to exonerate him or condemn him. I didn't know anything." — Reuters