• Government bond markets in France saw some selling early on Monday, but were fairly muted overall.
• The relative calm comes despite France facing a challenging fiscal position.
• David Roche, president and global strategist at Independent Strategy, said in a note that a win for the left-wing alliance could actually be worse economically than a National Rally government.

Government bond markets in France saw some selling early on Monday, but were fairly muted overall despite political gridlock after a second round of legislative elections.

The yield, which moves inversely to the price, on the 10-year French government bond rose 3 basis points in early trade, but retreated shortly after and was relatively flat at 3.221% around 9:30 a.m. London time.

Jitters have spread through France's bond market in recent weeks. The 10-year yield topped 3.3% — a roughly 8-month high — after French President Emmanuel Macron called the snap parliamentary election in the middle of June.

Meanwhile, the gap (or spread) between French bond yields and German bond yields had topped 85 basis points in recent weeks, hitting its highest level since 2012.

After falling as the election approached, the gap on Monday widened to more than 70 basis points before slipping back to around 67 basis points.

The relative calm comes despite France facing a challenging fiscal position. 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 its debts.

This meant the tax and spending plans of both the left-wing New Popular Front and the hard-right Rassemblement National (RN, or National Rally) party had been a key cause of concern going into the snap election.

Results from the vote on Sunday showed the New Popular Front coalition unexpectedly won the most seats in the country's parliament but failed to clinch an absolute majority. French President Emmanuel Macron's Ensemble party and its allies came second, while the far-right Rassemblement National — which won the first round of elections and was expected to retain a strong momentum in the runoff vote — came in third place.

David Roche, president and global strategist at Independent Strategy, said in a note Sunday that 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.

François Digard, head of French equity research at Kepler Cheuvreux, said a hung parliament was mostly priced in by markets, although it will now be more left-wing than expected.

"We believe the reaction is going to be negative both on the indexes and on the spread as well, that is supposed to widen, maybe to go back where it was 10 days ago," he told CNBC.

He added that the chances of a confrontation with Brussels remained with the left-wing alliance, but not to the same extent as if the National Rally had won. Digard added that what is key now is who is named prime minister.

—CNBC's Jenni Reid contributed to this article.