Just a couple of weeks ago, France was under scrutiny over how it would plug the holes in its budget. Now the issue is whether the euro area's second largest economy can muster a budget at all.

What France does with its strained public finances will be an early test of whether it can still be governed after the hung parliament created by President Emmanuel Macron's move to call snap elections. Financial markets, the European Commission and its euro zone partners are all watching closely.

Already, constitutional geeks are poring over obscure texts to find a way out of the impasse. One even raises the prospect of any new government getting a monthly pass to keep basic public spending flowing along lines set by the old budget.

It gets harder this week as lawmakers return to Paris from the provinces with their versions of what voters told them - in an election where few dared mention the inconvenient truth that France is already way above its EU-mandated deficit limits.

"A divided National Assembly will find it hard to agree on politically difficult spending cuts," said Leo Barincou, senior economist at Oxford Economics, referring to France's parliament.

"This will put France on a collision path with the EU's new fiscal rules," he added of deficit limits which, even with more generous deadlines, France was already seen struggling to keep.

Already the IMF and France's own budget watchdog doubted the outgoing government's plans to get last year's deficit of 5.5% of output down to the EU ceiling of 3% by 2027 - when far-right leader Marine Le Pen is widely expected to run for president.

Election gains made by a left-wing alliance on a hefty tax-and-spend ticket in theory nudge the political momentum even further from budget thrift - as does the fear that the slightest whiff of austerity will boost Le Pen's Elysee Palace ambitions.

Some scenarios have Macron's centrists and possibly moderate conservatives cooperating with leftists to back some modest spending plans either on a vote-by-vote basis, a grand coalition or inside a minority government.

They could wield the infamous Article 49.3 which Macron used to ram last year's unpopular pension reform through parliament, or the lesser known Article 47 which also allows budget bills to be passed by decree after 70 days of parliamentary deadlock.

But given that none of France's anti-far-right forces - centre, left or mainstream right - have anywhere near a majority by themselves and hold such divergent views, that would take consensus-building rarely ever seen in French politics.

"We need to deliver on what French voters want, be it the health of the economy, be it wages," said Eric Woerth, a former right-winger who joined Macron's camp. "But it will take time. Everything needs to calm down."

"Welcome to coalition politics," said Nicolas Véron, senior fellow at Brussels's Bruegel think tank and the Peterson Institute for International Economics in Washington.

"It may take protracted talks and a lot of trial and error," he said of the government formation spectacle more often seen in neighbours such as Italy, where some prime ministers have had shelf lives measured in days or weeks.

SUMMER OF DISTRACTIONS

If no way forward emerges, the constitution requires a delay of one year before new elections. That would usher in a period of paralysis well beyond the budget and into other policy areas, perhaps under a technocratic government with no real mandate.

Macron, who has so far stayed out of the post-election fray and risks political irrelevance for the remainder of his term, may use his July 14 Bastille Day address to appeal for lawmakers to seek solutions when they return to parliament a few days later.

But they will have little more than a week to make headway before attention is distracted by France's hosting of the Olympics Games and then the August holiday period - during which time French politics typically close down.

Bruno Cavalier, chief economist at Oddo Securities, said investors would demand higher premiums to hold French debt as the stasis continued, with credit agencies Moody's and S&P Global both this week citing their concerns.

The saga will take a new turn after the summer break with France then normally required to submit a draft budget to the European Commission by around mid-October.

How credibly that budget sticks to deficit-cutting pledges - and any slack cut to Paris by the Commission if it doesn't - will be watched no more closely than in Italy, one of seven European countries including France with excess deficits.

Prime Minister Georgia Meloni, who promised to bring Italy's 7.4% fiscal gap inside the EU's limit in 2026, is herself facing a tough task to draw up a 2025 budget that keeps the deficit on a downward path while keeping her pledge not to hike taxes.

Some of her coalition allies were already quick to spot a possible shift in the sand as it became clear that high-spending leftists emerged first in Sunday's run-off vote in France.

"Goodbye to European deficit rules," Claudio Borghi, a senator with Italy's co-ruling League party, posted on X.

(Additional reporting by Elizabeth Pineau and Michel Rose in Paris; Gavin Jones in Rome; Writing by Mark John; editing by Richard Lough and Susan Fenton)