Commentator Martin Couturie compared Lemerre with former socialist Prime Minister Lionel Jospin, who said he would quit politics after his defeat by far-right leader Jean-Marie Le Pen in the first round of the presidential elections on April 21.
"There is no need, no urge to pull out the daggers today," said Couturie.
"But, for the sake of honour, the team's coach must follow the path traced by Lionel Jospin, another 'coach' unable to survive a fateful first round."
The Communist daily L'Humanite agreed, calling France's campaign "an incomprehensible fiasco".
"No group can suffer such a Waterloo without the responsibility of the coach being called into question," it said, referring to the site of Napoleon's final defeat in 1815.
Liberation raised a glimmer of hope for the future, however.
"France did not win its second title as world champion, but
it is lucky enough to have training schools that are successfully shaping the generation that will replace the fading stars of this World Cup," it said.
"It's just a question of time."