The poll published in Le Figaro newspaper showed 33 percent of respondents were confident in the current leaders' ability to fight terrorism, down sharply from confidence levels of at least 50 percent in the wake of two major attacks last year.
"The government promises us things but nothing sticks," Nice city resident Antony Fernandez told Reuters TV. "What have they done up to now to make us feel safe? And yet what do we expect? Every six months we're going to mourn for more dead?"
The latest poll came at a moment when, less than a year from a presidential election, political opponents have fast abandoned the initial restraint that usually prevails on such occasions to sharply criticise Hollande and his government.
Ex-president Nicolas Sarkozy, who is competing in a November primary for the ticket to run as presidential candidate for France's mainstream centre-right parties, said overnight Hollande's government had failed to do all it could.
"I know there's no zero risk, I know perfectly well that we don't pull each other apart before the victims have even been buried," he told TF1 TV.