The French Prime Minister, Mr Jean-Pierre Raffarin, has called for vigilance against extremism, racism and anti-Semitism and warned that French society had already lost some of its bearings.
Mr Raffarin, speaking at his first major news conference since conservative President Jacques Chirac named him prime minister in May, said his government's moves to ban a violent far-right group showed how seriously it took the extremist threat.
The government has begun proceedings to ban Unite Radicale, a white supremacist group supported by the neo-Nazi who fired a shot in Mr Chirac's direction during the Bastille Day parade on July 14th. He missed by a wide margin and was promptly arrested.
Earlier this year, a wave of anti-Semitic attacks linked to violence in the Middle East brought criticism from Jewish groups, who said Paris was not taking aggression against Jews seriously.
"We have to be particularly vigilant about anything that could let extremism develop, anything that could lead to xenophobia, anti-Semitism and racism," Mr Raffarin said.
"I'm very attentive to these issues because I sense that our society today has lost some of its bearings. We have to remind everyone that the French republic brings people together."
France's traditional values of liberty, equality and fraternity have come under pressure in recent decades as the country struggled to integrate Arab and African immigrants.
Far-right leader Mr Jean-Marie Le Pen stunned France when he entered the second round of a presidential election before being beaten in May as mainstream voters rallied round Mr Chirac.
Rising crime, often among disadvantaged youths of Arab origin, was a major issue in those polls and the election that brought Mr Raffarin's centre-right government to office.