President Chirac's Union for the Presidential Majority (UMP) coalition is poised to seize control of the house after picking up 43.6% of the vote in the first round on Sunday, compared with 36% for the mainstream left, which had dominated the last parliament.
But nearly 35% of voters, a national record, stayed at home, giving hope to the left that there could still be surprises next Sunday, if they can mobilise their supporters.
Socialist Party leader Francois Hollande appealed to those who had abstained to help "avoid a dangerous imbalance in our democracy", stemming from a massive centre-right parliamentary majority.
"The remobilisation of those voters who perhaps didn't see exactly what was at stake in the first round is now key," he said.
Time out
But voters appear keen to end five years of "cohabitation" - the awkward co-existence between Mr Chirac's right-wing presidency and a left-wing parliament and government.
If the centre right does emerge triumphant after next week's poll, Mr Chirac will become one of the most powerful presidents in recent French history - with control over the National Assembly as well as the Senate.
The Socialists meanwhile are still reeling from their defeat in the presidential election by the far right, and the subsequent resignation of their leader, presidential candidate Lionel Jospin.
Despite a sound record of achievements in government, correspondents say that the left has come across as leaderless since Mr Jospin's departure from the helm.
Some observers even feel it would be to the Socialists' advantage to stay out of power for the next legislative term, avoid the series of tricky and unpopular issues that lie ahead of the next government and formulate a new identity for themselves.
Nuisance factor minimised
The second round of the elections is due to take place on 16 June, when all candidates who garnered more than 12.5% of the vote in the first compete in a run-off.
The National Front could still prove a nuisance to Mr Chirac's conservative forces in seats where the far right, the centre right and the left have entered the second round, by splitting the right-wing vote.
This could allow the left-wing candidate to slip through.
However, the number of seats where this could happen is dramatically fewer than had initially been anticipated, due to a performance poorer than expected from Mr Le Pen's National Front (FN), which picked up just 11.2% of the vote.
This is around five points lower than his showing in the presidential election and also worse than the party's showing in the 1997 general election.
The FN will contest only 37 races in the second round, far from the 300 Mr Le Pen said were in reach.