Conservative parliamentarians, drafted in after Dominique de Villepin, the prime minister, failed to rush the reform past stiff public opposition, have offered no-holds-barred talks on the First Job Contract (CPE) but not suggested scrapping it.
The unions said Tuesday's protests rang the death knell for the law making it easier for employers to hire and fire young workers.
They reported more than three million marchers across France on the fifth national protest day. Police put the turnout at just over one million.
The 12 main unions are to discuss strategy on Wednesday morning before the first meeting with leaders of president Chirac's Union for a Popular Majority (UMP) in the afternoon.
The business daily Les Echos gave voice to growing concern in business circles that Chirac and Villepin had badly mishandled a crisis which has begun to hit French order books.
"The confusion caused by the executive and the bizarre way that part of its power was transferred to the UMP did not discourage the protesters," it wrote.
"Dominique de Villepin promised in January that 2006 would be 'a useful year.' Today, that's not the most probable outcome"
French business daily
"Nobody is looking with enthusiasm at the 12 long months that separate us from the next presidential election. Dominique de Villepin promised in January that 2006 would be 'a useful year.' Today, that's not the most probable outcome."
The headline in the popular daily Le Parisien was blunter: "What is Villepin good for?"
Laurence Parisot, head of the Medef employers group, said on Tuesday that the protests, coming after suburban riots last autumn, were hurting trade as France's image soured abroad.
Parisot said that "we have to realise that this threatens the economy of our country ... and ask ourselves how we get out of this unfortunate situation as quickly as possible."
Police detained 383 people in
post-march clashes in Paris
Though most marches passed off peacefully, 383 people were arrested in post-march clashes in Paris.
Arrests were also made in the western city of Rennes after youths stoned police.
Villepin championed the CPE "easy hire, easy fire" jobs law as a tool to cut youth unemployment of 22%. But critics say by allowing firms to lay off under-26s any time in a two-year period the measure would fuel job insecurity.
Anxious not to lose his prime minister with a year to go to presidential elections, Chirac has thrown his weight behind Villepin despite misgivings about his choice of tactics.
But Villepin's approval ratings have slumped 20 points to 28% in two months, according to a new poll, and badly hurt his thinly veiled ambition to run for president in 2007.
Chirac has effectively sidelined Villepin, the long-time aide who advised him to hold the snap parliamentary election in 1997 that his party lost, and cast the UMP in the unlikely role of crisis mediator with union bosses.
Delegating such responsibility to deputies goes against the nature of France's Fifth Republic, which General Charles de Gaulle designed in 1958 with a powerful president, a subordinate prime minister and a weak parliament.
In a letter to the union confederations, UMP parliamentary leaders Bernard Accoyer from the National Assembly and Josselin de Rohan from the Senate offered to debate "without bias" a new draft law designed to modify the CPE.
The UMP's frontline role has
enhanced Sarkozy's influence
Meetings were due to start at 1300 GMT.
Accoyer and Rohan, two politicians little known outside Paris political circles, were to meet representatives from student bodies and employers' groups after talks with the unions.
The UMP's frontline role has enhanced the influence of Interior Minister Nicolas Sarkozy, the UMP leader and Villepin's bitter rival to lead conservatives in the presidential polls.
Last autumn's riots temporarily hit confidence in the euro zone's second biggest economy before bouncing back.
On Friday, Thierry Breton, the finance minister, said the current difficulties had not hurt the economy, despite data showing the contrary.