Despite France facing political gridlock, its bond markets remain stable.

• On Monday, the French government bond markets experienced some selling early on, but overall, the activity was subdued.
• The relative calm comes despite France facing a challenging fiscal position.
• According to David Roche, president and global strategist at Independent Strategy, a victory for the left-wing alliance could have a more negative impact on the economy than a National Rally government.

Despite political gridlock following the second round of legislative elections, government bond markets in France experienced minimal activity on Monday.

The price of the 10-year French government bond decreased by 3 basis points in early trade, but later returned to a flat rate of 3.221% at 9:30 a.m. London time.

In recent weeks, anxiety has increased in France's bond market, causing the 10-year yield to reach a 8-month high of 3.3% following French President Emmanuel Macron's announcement of a snap parliamentary election in June.

The gap between French and German bond yields has surpassed 85 basis points in recent weeks, marking its highest point since 2012.

As the election neared, the gap on Monday increased to over 70 basis points before narrowing to approximately 67 basis points.

Despite facing a challenging fiscal position, France has maintained relative calm. The European Commission recently announced that it planned to launch an Excessive Deficit Procedure against France due to its failure to keep its budget deficit within 3 percent of gross domestic product. An EDP is an action taken by the European Commission against any EU member state that exceeds the budgetary deficit ceiling or fails to reduce its debts.

The tax and spending plans of the New Popular Front and Rassemblement National party were major concerns in the upcoming election.

On Sunday, the New Popular Front coalition won the most seats in the country's parliament, but fell short of an absolute majority. The Ensemble party, led by French President Emmanuel Macron, came in second, while the far-right Rassemblement National finished third.

According to David Roche, president and global strategist at Independent Strategy, a victory for the left-wing alliance could have a more negative impact on the economy than a National Rally government.

He advised against shorting French government bonds and recommended shorting German bonds, stating that any relief from a far-right RN victory would be fleeting.

Kepler Cheuvreux's French equity research head, François Digard, stated that markets had mostly priced in a hung parliament, but the resulting government will be more left-wing than anticipated.

He stated to CNBC that he expected the reaction to be negative on both indexes and spread, with a possible widening that could bring it back to its 10-day-ago level.

Digard stated that the likelihood of a confrontation with Brussels is still with the left-wing alliance, although not as intensely as if the National Rally had won. What is crucial now, according to Digard, is who will be named prime minister.

—CNBC's Jenni Reid contributed to this article.