Jean-Yves Le Drian warned that Paris and its allies were losing patience and could review financial aid to the economically troubled country.
Lebanon has been without a president for almost a year after Michel Aoun's mandate expired last October. The current parliament, one of the country's most deeply divided, has failed 12 times to elect a successor, with competing blocs backing two different candidates.
"The life of the Lebanese state itself is at risk," Mr Le Drian, a former French foreign minister, told AFP in an interview.
The rival sides have put forward their own candidates, with the pro-Hezbollah faction backing Marada leader Suleiman Franjieh and their opponents backing former minister Jihad Azour.
Mr Le Drian said neither candidate had a chance of breaking the deadlock.
"Neither side can prevail. Neither solution can work," he told AFP.
Faced with what he described as a "denial of reality" from Lebanese officials, France and allies the US, Saudi Arabia, Qatar and Egypt, are losing patience, Mr Le Drian said.
The five countries, whose representatives met on the sidelines of the UN General Assembly last week in New York, "are totally united, deeply irritated and questioning the sustainability of their funding to Lebanon while political leaders take pleasure in irresponsibility," he warned.
Parliamentary struggle for power
An official in the anti-Hezbollah Lebanese Forces rejected Mr Le Drian’s accusation that both blocs were at fault for the parliament’s failure to elect a president.
“We are presently looking forward to an agreement on a third name that can bring sovereignty to the country,” the official said.
The Lebanese Forces-led bloc has placed the blame squarely on its rival’s unwillingness to compromise on Mr Frangieh.
“They [Hezbollah] want the Lebanese to surrender to their rule,” the official said.
Mr Frangieh, leader of the Christian Marada movement, is a close ally of Hezbollah.
The Lebanese Forces-led bloc maintains it has been flexible in proposing candidates.
Mr Azour is its second since last October, after former candidate Michel Moawad failed to receive the required number of votes in Parliament.
The bloc says Hezbollah and its allies want to impose a malleable candidate.
“We are ready to discuss anyone qualified for the presidency if it gets Lebanon on course for reform and rescue,” the official said, qualifying that they would only consider candidates not beholden to not a political party’s agenda.
Hezbollah has called Mr Azour a "confrontation and challenge candidate,” claiming the rival side used a "guise of flexibility" to try to impose its own candidate.
"The other team is trying to impose a president who bears the characteristic of confrontation,” Hezbollah MP Hassan Fadlallah said in June.
The Lebanese Forces official told The National, that in the absence of the rival bloc’s willingness to compromise, there are limits to their flexibility:
“We are not going to entertain them by seeking a fourth and fifth candidate,” the official said. “Until they really commit to entering Parliament and electing a president.”
Lebanon's president is elected by a sitting parliament, but neither side has a clear majority.
Parliament has now failed 12 times to elect a president over the past year, with both blocs claiming the other is obstructing the democratic process.
Mr Le Drian said he planned to visit Lebanon in the coming weeks to urge rival parties to convene for a week of talks and then hold votes in parliament to find a new president.
But the Lebanese Forces-led opposition had previously rejected an initiative by Parliament Speaker Nabih Berri – also leader of the Hezbollah-allied Amal movement – to hold a week-long dialogue prior to holding elections, on the grounds that dialogue should take place in parliamentary sessions.
“If they were pro-dialogue they would contribute to democratic life and the internal regulations of the parliament,” the LF official said. “But they’re not. It’s Frangieh, Frangieh, Frangieh.”
Mr Le Drian, who was named by Mr Macron as his special envoy in early June, has made two visits to Lebanon in his capacity, in June and July. But he has so far failed to make inroads in breaking the deadlock.
Mr Le Drian declined to suggest a candidate who could break the deadlock to AFP, saying that he is only a "mediator" and that it is up to the Lebanese to identify a compromise.
Sanctions against those who block compromise remain a possible tool to apply pressure.
"It's obviously an idea.”
With reporting by agencies.