Turnout was low, interior ministry data showed. Many of those who voted for him in the presidential election, particularly left-wing voters, said they were doing so only to keep Marine Le Pen out.
A swath of senior Socialists, including former government ministers, lost their seats in the first round.
Cambadelis called on voters to favor more political pluralism in the second round.
French President Emmanuel Macron will win a crushing majority in Parliament in a week's time, according to projections from his En Marche party's first-round victory last night.
"France is back", Prime Minister Edouard Philippe declared triumphantly.
After the projections were announced, a government spokesman said voters had shown they wanted to move fast on major reforms.
The weak turnout will likely narrow the second-round field, because candidates need the support of 12.5 per cent of registered voters to qualify.
She hopes to be a strong opposition force, but her party is only projected to hold about a dozen seats.
Despite the poor performance, Le Pen's control over the party remained too strong for any challenge to her leadership in the near future, he said, especially after her niece Marion Marechal-Le Pen stepped away from politics.
Sebastian Vettel 'disgraced' himself with car chop in Baku, claims Lewis Hamilton
It is all just noise in the background, I don't care. "I had to overtake everyone". "It just shows you should never give up. It was an extraordinary performance from Stroll, the son of a billionaire, who faced heavy criticism earlier in the season.
His fledgling Republic on the Move! - contesting its first-ever election and fielding many candidates with no political experience at all - was on course to deliver him a legislative majority so crushing that Macron's rivals fretted that the 39-year-old president will be able to govern France nearly unopposed for his full five-year term.
The near-final first-round tally pointed to a legislative majority so crushing that Mr Macron's rivals fretted that the 39-year-old president will be able to govern France nearly unopposed for his full five-year term.
With 94 per cent of votes counted, the president's camp was comfortably leading with more than 32 per cent - putting it well ahead of all opponents going into the decisive second round of voting next Sunday for the 577 seats in the lower-house National Assembly.
Far-right National Front led by Marine Le Pen has come in third in terms of the popular vote but is projected to win only between 1 and 5 seats.
According to the latest polls, Macron's movement appears in a position to win potentially as many as 400 seats.
France goes to the polls today with President Emmanuel Macron seeking the parliamentary majority he requires to bring about his political revolution.
Le Pen and other opposition figures chose instead to highlight the abstention rate, which the National Front leader described as "catastrophic", calling on "patriots" to turn out "massively" in next Sunday's second round, which will fill most of the assembly's seats.
Jean-Christophe Cambadelis, head of the Socialist party that was in power until a month ago, acknowledged that the first round marked an "unprecedented" setback for the party, set to win a paltry 30-40 seats, and the broader left. Mr Macron wants a powerful mandate to push through plans to reduce worker protections to boost hiring, boost security and clean up corruption in politics. In France's last legislative elections, in 2012, turnout in the first round stood at 57.22 percent. The year 1978 saw the highest participation in a first-round legislative vote, with 83.3 percent of voters casting a ballot.
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