Projections after the first round of France's parliamentary elections suggest President Nicolas Sarkozy's party is heading for a landslide.
Nicolas Sarkozy looks set for the big majority he is depending on
Although most seats will not be decided until next week's second round, polling firms said Mr Sarkozy's UMP party would win at least 383 of the 577 seats.
Analysts say a big majority would allow the new president to press ahead with his sweeping economic reforms.
Turnout is reported to have reached a record low, at around 61%.
That contrasted with a turnout of 84% at the presidential election a month ago.
"Many people seem less interested in the parliamentary elections because they think Sarkozy will win a large majority anyway," Mikhael Perez, a 48-year-old voter from Paris told Reuters news agency.
With a second round of voting to follow next week, the size of the UMP's likely majority was still uncertain.
Many voters will return to the polls for 17 June's second round
Polling companies said the party could win anything between 383 and 501 of parliament's 577 seats, compared to its 359 at present.
Mr Sarkozy's Prime Minister, Francois Fillon, said: "Today you have chosen to give the presidential majority a beautiful lead... Tonight we have gone some of the way.
"But everything will really be decided next Sunday. This is why all the French need to go to vote. Change is on the march."
The Socialists, whose presidential candidate Segolene Royal lost to Mr Sarkozy, appeared set for another big disappointment.
It was predicted they could lose some of their 149 seats - and possibly as many as half of them.
Ms Royal urged left-wing voters to show up next weekend. "The republic needs you, because the republic needs a great force of the left to watch over things," she pleaded.
If candidates do not win more than 50% of the vote, with at least a 25% turnout, the constituency must vote again on 17 June.
Most will go to a second round. Any candidate with a first-round score of 12.5% or more of the registered vote is eligible to stand.
France has not returned the same government to power since 1978 - but this time the pattern looks set to change, the BBC's Emma Jane Kirby in Paris says.
France's "blue wave" means the president will get exactly what he wants - strong backing with which to implement his ambitious programme of economic reforms, our correspondent adds.
The parties of the left - including the communists, who look set for their worst result in memory - have called for a big turnout next week, warning voters not to give absolute power to Nicolas Sarkozy.
"He is a sort of hyper-president," said Socialist Pierre Moscovici, a member of the European parliament.
Mr Sarkozy has said he will hold a special session of parliament in July to initiate his first set of political reforms, which include tougher immigration rules and more freedom for universities.
A new finance bill will mean that overtime earnings are no longer taxed, inheritance tax is abolished for most people and overall individual taxation is capped at 50%.