• In the run-up to the second round vote, analysts at Citi warned that stock markets may be slightly too optimistic about the French election.
• Analysts at investment firm Daiwa Capital Markets also spoke of uncertainty, if no single party managed to gain an absolute majority.
• France is facing a challenging fiscal position and the European Commission announced two weeks ago that it intended to place France under an Excessive Deficit Procedure.

Initial indications on Sunday evening for the French parliamentary run-off vote threw up some big surprises, leaving political commentators contemplating a "hung parliament" scenario that could prove challenging for both policymaking and financial markets.

France's left-wing New Popular Front coalition is seen by some projections to gain the most seats in the election, with French President Emmanuel Macron's Ensemble party and its allies in second place, and with the far-right Rassemblement National coming in third. With none of the groups expected to hit the 289 seats needed for an absolute majority, gridlock could ensue over the coming weeks.

The euro slipped about 0.3% against the U.S. dollar in thin trading on Sunday evening after the exit polls were released.

In the run-up to the second round vote, analysts at Citi warned that stock markets may be slightly too optimistic about the French election and that "higher-probability outcomes" such as a deadlock "would imply somewhere between 5-20% lower equity market valuations."

"Combined with our finding that French equities tend to be more volatile than peers' around elections, this could be reason to expect additional choppiness from here ... For context, a 10% move in French equities is usually accompanied by an 8% move by the overall Stoxx 600," the analysts said in a note dated June 26.

Analysts at investment firm Daiwa Capital Markets also spoke of uncertainty if no single party managed to gain an absolute majority. In a research note earlier this week, the analysts said a grand coalition of the moderate left and center parties, a unity government or a minority government were all feasible outcomes.

"Regardless, uncertainty about the outlook for French policymaking is likely to be long-lasting," the analysts said.

Concerns on spending

The tax and spending plans of the left-wing New Popular Front and the hard-right Rassemblement National (RN, or National Rally) party have been a key cause of concern since the snap election was announced.

France is facing a challenging fiscal position, and the European Commission announced two weeks ago that it intended to place France under an Excessive Deficit Procedure due to its failure to keep its budget deficit within 3 percent of gross domestic product. An EDP is an action launched by the European Commission against any EU member state that exceeds the budgetary deficit ceiling or fails to reduce their debts.

"A fractious parliament means that it will be difficult for any government to pass the budget cuts that are necessary for France to comply with the EU's budget rules and put its public debt on a sustainable path," Jack Allen-Reynolds, deputy chief euro zone economist at Capital Economics, said in a note immediately after the exit pols were released.

"The chance of France's government (and the governments of other countries) clashing with the EU over fiscal policy has increased now that the bloc's budget rules have been re-introduced and several countries – including France and Italy – are set to be put into Excessive Deficit Procedures," he added.

Bond rout

Jitters have spread through France's bond market in recent weeks. The premium on the country's borrowing costs compared to those of Germany has recently been trading at its highest level since 2012.

France's benchmark 10-year government bond yield has also risen above 3.3%, roughly an 8-month high, since the snap election was called by Macron in the middle of June.

David Roche, president and global strategist at Independent Strategy, said in a note Sunday that the early indications of a win for the left-wing alliance could actually be worse economically than a National Rally government. He said that any relief at avoiding a far-right RN outright victory will be short lived and recommended shorting French government bonds versus German bonds "where the spread is only 70 basis points."

Shorting involves betting that the price of an asset will fall.

"This is a hung parliament with some sort of shaky alliance negotiated by discredited president but no policy agenda," he said.

Holger Schmieding, chief economist at Berenberg Bank, sees a hung parliament as the most likely and least negative scenario since the election was first announced by Macron.

"However, it is still not a good outcome, to put it mildly. It spells the end of Macron's pro-growth reforms. Any government, whether still led by the current prime minister Gabriel Attal – or perhaps by a candidate more palatable to the centre-left – will struggle to get much done," his team of analysts said in a recent research note.

Shane Oliver, the chief economist and head of investment strategy at AMP, said that a hung parliament would not be good in terms of reforms and reducing the deficit. But, he said, it could be seen as a least bad outcome for markets "as it would reduce the chance of a conflict over fiscal policy and head off extremist NR policies."

—CNBC's Jenni Reid and Holly Ellyatt contributed to this article.

Correction: This story has been updated with the the correct historical data for French bond yields.