The office of Prime Minister Jean-Pierre Raffarin ordered the flags on France's public buildings be lowered for 24 hours following the death of the Pope late on Saturday, "in keeping with Republican custom".
But critics said French Republican custom was secular, and pointed to France's law banning conspicuous religious symbols in classrooms to underscore the point.
"The French Republic should not descend to such a level," said Socialist Senator Michel Charasse, a former finance minister. "If the Dalai Lama were to die tomorrow, would we lower the flags to half-staff?"
The communist mayor of Aniane refused to put flags in the picturesque village in southern France at half-staff in the name of secularism, the mayor's office said.
Cardinal Bernard Panafieu of Marseille said, however, lowering the flags "in no way damages secularism, which we ourselves strongly support. It's simply a sign that there are people in the world who transcend ideologies and borders because they are men of peace and reconciliation".
"It isn't written 'Catholic France' or 'the Catholic Republic of France' like the Islamic Republic of Iran"
deputy mayor for culture
The debate was taken up on national television discussion programmes.
"I'm troubled," Christophe Girard, deputy mayor for culture at Paris City Hall, told France-2 television. "On the front of our town halls, our schools, it is marked liberty, equality, fraternity.
"It isn't written 'Catholic France' or 'the Catholic Republic of France' like the Islamic Republic of Iran," said Girard, a Green Party member who describes himself as Catholic.
Government spokesman Jean-Francois Cope dismissed the objections, saying he regretted the debate which "shouldn't even be taking place".
"John Paul II was an exceptional man, a man of peace," Cope said. Putting the flags at half-staff is "a simple act of homage by the republic".
The attendance by President Jacques Chirac and other top officials at a memorial service for the Pope on Sunday in Paris' Notre Dame Cathedral also raised eyebrows.
France is a largely Roman Catholic country with Western Europe's largest population of Muslims and of Jews.
A controversial French law
barred hijab in public schools
This year it is marking the 100th anniversary of the 1905 law separating church and state that culminated a hard-fought battle with the clergy.
Last year, France passed a controversial law banning religious symbols in public schools, including Muslim headscarves, large Christian crosses and Jewish skullcaps. Critics said it infringed freedom of expression. However, its defenders cited the secular nature of modern-day France.
Socialist Senator Jean-Luc Melanchon said the government's move was inopportune, "a sort of favour made to one religion".
"The state authorities must demonstrate an absolute secularism without shades or halftones," said Melanchon.
"The large majority of the French belong to no religion."
Olivier Besancenot, spokesman for the far-left Revolutionary Communist League, said: "When we speak of religion in France, there shouldn't be any double standards."