President Emmanuel Macron met left-wing leaders on Friday, at the start of two days of crunch talks aimed at deciding who will form France's next government.
Snap elections in early July left French politics in deadlock, with no party able to form a clear majority in the National Assembly.
A caretaker government led France during the Paris Olympics, to the anger of a left-wing alliance that topped the poll.
Their four-party New Popular Front wants a little-known senior civil servant called Lucie Castets to be named prime minister. However, the 37-year-old economist is unelected and seen as an unlikely presidential pick for prime minister.
Under France's political system, the president appoints a prime minister who can command a majority in the National Assembly. In recent years, that prime minister has come from the same party as the president, because they are elected within a few weeks of each other.
But after Mr Macron stunned France in June by calling a snap two-round parliamentary vote, his centrist Ensemble alliance came runner-up behind the leftist NFP.
The Élysée Palace said ahead of Friday's talks that Mr Macron was "on the side of the French" and "the will of their vote". A large and stable majority is required that won't fall with the first censure motion, presidential officials were quoted as saying.
Arriving for talks with the president, along with the leaders of the far-left France Unbowed, the Socialists, Greens and Communists, Lucie Castets said they had come to remind the president to "respect the election result and bring the country out of the paralysis it has been plunged into".
She said afterwards that she and her colleagues were satisfied that the president had understood that French voters had sent a message at the elections that they wanted a change of political direction.
"Nevertheless the president still seems to be tempted to form his government - we told him it was up to the political force that came top, the New Popular Front, to form a government," Ms Castets said.
Socialist leader Olivier Faure said the president had not given a precise date for naming a prime minister, but said it would be quick.
Mr Macron was next due to meet the parties that make up his own Ensemble alliance followed by the leaders of the right-wing Republicans.
On Monday he will talk to the leaders of the far-right National Rally, Marine Le Pen and Jordan Bardella, along with Eric Ciotti, who heads a group of Republicans who split from the rest of the party before the election. They came third in the election, even though they had led the first round.
No party grouping has enough seats to make up the 289 required for an absolute majority in the 577-seat National Assembly.
But under the constitution Mr Macron cannot dissolve parliament until next summer, so analysts believe he is likely to name as prime minister a figure who would have the best chance of finding common ground among the parties.
In a letter to the French people last month he said voters had expressed their desire for change and broad political unity.
Among the names discussed in political circles are former Socialist interior minister Bernard Cazeneuve and Xavier Bertrand, who is a regional leader from the Republicans.
However, Mr Macron has not given any indication yet of who he might support.
Almost seven weeks after the election, and a supposed political truce that he called during the Paris Olympics, he now has the difficult task of finding a candidate who can form a government that does not collapse at the first sign of a vote of no confidence.
