PARIS, July 9, 2024 (BSS/AFP) - France's political parties sought to project strength and gather allies on Tuesday, with the government adrift following a Sunday parliamentary election in which no one force claimed a clear majority.

Having defied expectations to top the polls, new MPs from the left-wing New Popular Front (NFP) alliance were set to show up in force at the parliament building throughout the day.

But the coalition of Greens, Socialists, Communists and the hard-left France Unbowed (LFI) is still debating over who to put forward as a potential prime minister and whether it could be open to working in a broader coalition.

Combined, the left-leaning parties' 193 of 577 seats in the National Assembly are well short of the 289-seat threshold for a majority.

Socialist Party chief Olivier Faure on Monday said that members should come up with a potential prime minister "within a week" to avoid "leaving a vacuum" for President Emmanuel Macron to occupy.

In the French system, the president nominates the prime minister, who must be able to survive a confidence vote in parliament -- a tricky proposition with three closely-balanced political forces in play.

Macron's camp came second in Sunday's vote, taking 164 seats after voters came together to block the far-right National Rally (RN) from power -- leaving the anti-immigration, anti-Brussels outfit in third place with 143 MPs.

The president has kept his prime minister Gabriel Attal's government in place for now, hoping that horse-trading in the coming days and weeks could leave an opening for him to reclaim the initiative.

However, "there has been an institutional shift. Everyone thinks it's up to the newly-elected National Assembly to bring forth a solution, which (Macron) would simply have to accept," wrote commentator Guillaume Tabard in conservative daily Le Figaro.

- 'Unprecedented situation' -

The new focus on parliament has led to a media frenzy in which "it's difficult to work calmly", Greens party chief Marine Tondelier complained.

"We're in an unprecedented political situation and so we have no set of instructions to follow," she added.

In a sign that some divisions remain, left parties' MPs planned to enter the parliament at different times throughout the day.

The Socialists are still hoping to glean a few more members for their group to outweigh LFI and have a greater say over the alliance's direction.

Meanwhile, members of Macron's camp were eyeing both the centre-left Socialists and conservative Republicans as possible allies of convenience for a new centrist-dominated coalition.

"We're in this situation where either every side says 'I want to govern by myself while representing just 30 percent of people'... or we manage to build a common roadmap, which doesn't mean we agree about everything," former parliament speaker Yael Braun-Pivet told broadcaster France Inter.

She suggested a temporary alliance could give voters the answers they need on a limited slate of issues including purchasing power, security and slimming down the state.

- What next? -

Even as politicians struggle to define the immediate path ahead, eyes are also already turning to the next time French voters will be called to the polls.

Macron's term expires in 2027 and he cannot run a third time -- potentially leaving the way open for his twice-defeated opponent, RN figurehead Marine Le Pen, to finally capture the presidency.

The far-right outfit has been digesting a disappointing result after polls suggested it could take an absolute majority in parliament.

On Tuesday, party sources told AFP its director-general Gilles Penelle had resigned.

Penelle, elected last month to the European Parliament, was the architect of a "push-button" plan supposed to prepare the RN for snap elections, which ultimately failed to produce a full roster of credible candidates.

But the far right outfit's progress is undeniable, having advanced from just eight MPs soon after Macron's first presidential win in 2017 to 143 today.

"Time is on our side," Le Pen's lieutenant and RN party chief Jordan Bardella said on Monday.

Macron himself has stayed above the fray, planning for a trip to Washington for a NATO summit starting on Wednesday where allies may be in need of reassurance of France's stability.