The far-left is demanding power after France avoided a far-right election win.

• Following the left-wing's victory in the French election, the focus has shifted to radical leader Jean-Luc Mélenchon, who has called for the left to seize the premiership.
• Last night, Mélenchon stated that the president holds both the authority and responsibility to summon the New Popular Front to take control.
• Since the snap election last month, economists have expressed concern about the expansionary fiscal policy of the left-wing New Popular Front.

Following the left-wing's election victory in France on Sunday, the focus has shifted to radical firebrand Jean-Luc Mélenchon, who has called for the left to be given the premiership and an opportunity to govern.

The New Popular Front (NFP) coalition, led by Mélenchon, won the most seats in France's second round of parliamentary elections. The NFP is made up of Mélenchon's France Unbowed party, the Socialist Party, the French Communist Party, and various green, center-left, and left-wing political groups. Despite being unexpected, the NFP successfully blocked the far-right's advance. Now, the NFP is positioning itself as a potential leader of a coalition government.

Last night, Mélenchon stated that the president has both the power and duty to call on the New Popular Front to govern, as it is ready for it, following exit polls indicating the NFP's victory.

The far-right National Rally and its allies won 143 seats in the second round of France's snap election, while the left-wing NFP gained 180 seats, but fell short of the 289 seats needed for an absolute majority in the 577-seat National Assembly. French President Emmanuel Macron's centrist "Together" bloc came in second with 163 seats.

After Prime Minister Gabriel Attal announced his resignation, France is facing a hung parliament on Monday morning, with a challenging road ahead to forming a new government or a technocratic government.

Mélenchon, who has previously praised Hugo Chavez and advocated for France to leave NATO and impose 100% tax rates on the country's wealthiest individuals, emphasized that the new prime minister should come from the left-wing alliance following his unexpected election victory.

According to political analysts and economists, it is highly unlikely that Macron, who has not yet commented on the election or his next step, will appoint Mélenchon as the new prime minister.

According to Antonio Barroso, deputy director of research at Teneo, the tradition of the largest party in parliament proposing a prime minister does not obligate Macron to pursue such an option.

"Mélenchon has stated that the new prime minister should come from NFP. Nevertheless, NFP lacks a leader, and the coalition partners are deeply divided on who they could choose."

If the NFP agreed on a figure and Macron appointed someone, the AN could still force a government collapse through a no-confidence motion, according to Barroso.

In order to achieve an absolute majority in the lower chamber of parliament, whoever is proposed as the new prime minister must gain the support of centrist parties. This means that a radical figure like Mélenchon cannot be appointed.

Economists expect a centrist

Since the defeat of his party in European Parliament elections in early June, economists have expressed concern about the expansionary fiscal policy of the left-wing New Popular Front.

The European Commission has announced that France will face an Excessive Deficit Procedure due to its failure to keep its budget deficit within 3% of GDP. If approved, France will have to present amended budget plans by mid-September.

Tina Fordham, founder of Fordham Global Insight, stated in a note that Mélenchon, despite being less well-known outside of French politics than Marine Le Pen of the far-right National Rally, has proposed a program with significant increases in public spending, a lower retirement age, and policies that conflict with the EU. This program is estimated to cost an additional 179 billion euro ($194 billion), according to the Institut Montaigne. However, Fordham noted that Mélenchon and other leftist alliance leaders are not market-friendly.

Allianz's chief economist, Ludovic Subran, stated that the far-left within the NFP faced a lot of opposition and that the more moderate side of the alliance would become more prominent during coalition negotiations.

"I'm not overly concerned, as I believe we are moving towards a center-left policy approach. France last adjusted its deficit during Francois Hollande's presidency, so positive changes can occur under a center-left government in France's European context," he said to CNBC's Charlotte Reed.