In his first major speech since rioting began, Mr Chirac spoke of a "crisis of meaning, a crisis of identity".
He condemned the "poison" of racism, and announced measures for the training of 50,000 youths in 2007.
Mr Chirac said he would uphold law and order by bring rioters to justice and cracking down on illegal immigration.
He also confirmed that the government of Prime Minister Dominique de Villepin would ask parliament to extend an emergency law allowing the imposition of curfews in towns across the country.
The president spoke as police and local authorities around France waited anxiously for proof that the prolonged period of violence is coming to an end.
Some 284 cars were burned on Sunday night, down from a peak of over 1,000 a week earlier.
A measure of calm has returned to Paris, although there was trouble in Toulouse and some remote towns.
Speaking at the Elysee Palace in front of the flags of France and the EU, Mr Chirac said the wave of violence had highlighted a "deep malaise" within French society.
"We are all aware of discrimination," the president said, calling for equal opportunities for the young and rejecting suggestions of a US-style quota system.
"How many CVs are thrown in the waste paper basket just because of the name or the address of the applicant?"
He was quick to defend the rule of law, sternly criticising those who turned to violence to vent their anger.
"Many French people have difficulties, but violence never solves anything. [If] one belongs to our national community one must respect the rules."
France would respond to the violence, Mr Chirac insisted, by staying faithful to the values of the Republic.
He called the rioters "sons and daughters of the Republic", but warned that respect among all French nationals was crucial to the long term strength of the nation.
"We will never build anything long-lasting without fighting this poison of racism."
Mr Chirac also warned that parents must work hard to ensure a respect for the law among their children.
"The justice system has been alerted," he added.
"Everyone must know that the law cannot be broken with impunity."
On Monday evening the far-right leader Jean-Marie le Pen led a protest against France's immigration laws.
Addressing a crowd of about 300 National Front supporters he criticised France's immigration policies.
"We let in 10 million foreigners over 30 years - it's wild insanity. No country can handle that invasion," Mr Le Pen said.
He said that France was now "paying the bill" for its "mad and criminal immigration from the Third World."