French President Emmanuel Macron and his allies on Monday began a crucial week of campaigning to save their parliamentary majority, under threat after a first round of voting that galvanised a newly formed leftwing alliance.

A strong showing by the left-wing NUPES coalition and gains by the far-right made it likely that Macron's "Ensemble" (Together) alliance could lose dozens of National Assembly seats in the second round of voting next Sunday.

"Macron's absolute majority threatened," Le Monde said in a front-page banner headline, also noting the record-low turnout of just 47.5 percent.

Macron's top lieutenants vowed to campaign hard against the "extremist" pledges of NUPES's leader, the hard-left veteran Jean-Luc Melenchon.

"We're going to make every effort to get a clear and strong majority, France needs it," his technocrat Prime Minister Elisabeth Borne said in Calvados, northwest France, where she is running for her first parliament seat ever.

Emmanuel Macron is facing the prospect of losing his absolute majority in parliament
Emmanuel Macron is facing the prospect of losing his absolute majority in parliament POOL via AFP / Ludovic MARIN

"There is a spending power crisis... we have a war at Europe's doorstep, we need stability," she said.

But for the left, which scored neck-and-neck with Macron's alliance in the popular vote at just over 25 percent each, "the second round is turning into an anti-Macron referendum," Eric Coquerel, a leading NUPES candidate, told LCP television.

Based on Sunday's results, Macron and his allies could emerge with 255-295 parliament seats, polling firms projected, well below the 345 it has currently.

Should Macron fail to win the 289 seats that would give him an absolute majority, he would need to win over right-wing opponents such as the Republicans for every legislative vote.

Macron will have to change his "vertical" style and work with "groups other than those who support him", political scientist Pascal Perrineau told AFPTV on Monday, while pollster Frederic Dabi said that a majority of voters appeared to want to deny Macron a parliamentary majority.

If so, that could complicate the centrist's plans for pushing back the retirement age to 65 as part of a pensions overhaul, as well as tax cuts or welfare reform.

Map showing the abstention rate by constituencies in the first round of the French legislative elections on June 12, according to the final results
Map showing the abstention rate by constituencies in the first round of the French legislative elections on June 12, according to the final results AFP / Kenan AUGEARD

Few analysts believe NUPES could secure its own majority, producing a "cohabitation" in which Melenchon would become prime minister and Macron would have a free hand only in international and defence policy.

But Melenchon does appear to have siphoned off voters disappointed with Macron's rightward tack in recent years, which earned the former investment banker the label of "president of the rich."

"It's not what is going to happen next Sunday, but we know that we're close to seeing the majority forced into a minority," veteran political expert Dominique Reynie at the Fondapol institute told Europe 1 radio.

Melenchon, who wants to lower the retirement age to 60 from 62, hike the minimum wage and create new taxes on the wealthy, would need to mobilise many more young voters, in particular, who stayed home in droves on Sunday.

Polling firms project that NUPES would hold 150-210 seats in the new parliament, making it the biggest opposition group.

Adding to Macron's worries: at least three of the 15 cabinet ministers running for parliament seats appear to be in trouble.

His high-profile Europe Minister Clement Beaune, Ecology Transition Minister Amelie de Montchalin, and Stanislas Guerini, Macron's party chief and civil service minister, are also at risk of losing next Sunday.

Ministers who fail to get elected will have to resign, according to French political conventions which Macron has vowed to uphold.

If his Together alliance fails to secure an absolute majority, its key players such as the popular former prime minister Edouard Philippe may demand greater sway in his cabinet.

That could result in a government reshuffle just a few weeks after Macron nominated Borne in the wake of his April re-election.