"It serves no purpose whatsoever to insult those people who chose far-right leader Jean-Marie Le Pen," declared the right-wing daily Le Figaro. The fact is, the paper continued, "an increasing proportion of the electorate is exasperated by the complacency and indifference of the political class."
Its political adversary, the left-wing Liberation agreed, drawing attention to a section of society who "consider themselves abandoned by governments and by the services of the state, forgotten by politics".
It was these people, the paper wrote, who had given their vote not just to Mr Le Pen, but to a range of extremist figures, including the ardent Trotskyite candidate Arlette Laguiller.
Social project
Seen in itself, the vote for the extreme-right should not be exaggerated, the paper noted, pointing out that Mr Le Pen had only marginally improved his position from the last presidential poll.
But faced with the fact that 30% of the French electorate had opted to back non-mainstream figures, it was clear that the time had come for "the recasting of French democracy, within the heart of Europe", the paper said.
The economic daily, La Tribune also called for a shake-up, demanding a new "social project" which would give fresh hope to the despairing unemployed, and to young people who had no goals in life.
Extremist voters were drawn from these groups, the paper argued.
"The French don't understand the meaning of what they have done, complain the Socialists. But they, have they understood the meaning of these votes?"
"They are readying themselves to continue to do the same things tomorrow as they did yesterday, with the same people."
The centre-left Le Monde cast its net wider, examining the results French election in the context of successive defeats of Social Democrat governments across Europe.
European far-right movements were not identical, it said, but all played on popular fears of immigration.
Europe's left-wing parties must now quickly come up with a credible and workable model to enable the integration of foreigners, the paper urged.
Sleaze
Le Figaro, hoped it would be incumbent president Chirac who seized the initiative for change in France.
"He has a historic opportunity: the chance to breathe new life into French democracy, to reconstruct the everyday workings of politics and to put forward the necessary reforms," said the paper, without specifying the exact content of such a reformation.
But Liberation said the upcoming battle between Mr Le Pen and Mr Chirac - which Mr Chirac is widely predicted to win - would not be an edifying one.
Mr Le Pen and his entourage will have no qualms about dragging into the foreground the sleaze and corruption allegations that date from Mr Chirac's years as mayor of Paris - topics that the Socialist rival, Lionel Jospin, chose to leave out of his failed presidential campaign.
"The victory expected by Chirac in the second round looks set to become the victory of Pyrrhus", referring to the king of Epirus who lost such a large part of his army in a battle in 200 BC to render his victory barely worthwhile.