President Emmanuel Macron faces a tough fight to win an absolute majority in parliament that would allow him to govern with a free hand after a strong showing by a new left-wing alliance in the first-round election.
Initial estimates by Elabe put the hard-left veteran Jean-Luc Melenchon's NUPES bloc neck-and-neck with Mr Macron's Ensemble! alliance in the first round, with 26.2 per cent and 25.8 per cent respectively.
Elabe projected Ensemble would go to win between 260-300 parliament seats - with the mark for an outright majority set at 289 seats - on June 19 and forecast the left would secure 170-220 seats, a big increase from 2017.
With rampant inflation driving up the costs of living and eroding wages, Mr Macron has struggled to build on his re-election in April, with Mr Melenchon casting him as a free-marketeer more intent on protecting the wealthy than hard-up families.
"In view of this result, and the extraordinary opportunity it offers us and the destiny of the common homeland, I call on people next Sunday to defeat the disastrous politics of the majority, of Mr Macron," Mr Melenchon said after the vote.
With the two-round system, which is applied to 577 constituencies across the country, the popular vote in the first round is a poor indicator of who will eventually win a majority the following week.
At stake is Mr Macron's ability to pass his reform agenda, including a contested pension reform that would see the French work longer, which he says is necessary to ensure long-term order to the public finances.
His opponents on the left are pushing to cut the pension age and launch a big-spending drive. Mr Melenchon's bloc has capitalised on anger over surging living costs and Mr Macron's perceived weakness at connecting with ordinary people.
The second round is on 19 June. Prime Minister Elisabeth Borne said "we have one week of action, one week to convince, one week to get a strong and clear majority".
Elsewhere, far-right leader Marine Le Pen won more than 55 per cent of the votes in her constituency, but will face a run-off because of rules on minimum turnout.
A record number of voters abstained, pollsters projected, with more than half of all registered voters staying away.
