In the French general election’s second round, the right-wing National Rally and its smaller associates garnered 10.1 million votes nation-wide — 37 percent of the voters. Yet they won only 143 seats out of 577 in the National Assembly. 

In sharp contradistinction, the left-wing New Popular Front got 182 seats with 7 million voters — 25.6 percent; the Macronist centrist coalition Ensemble 168 seats with 6.3 million — 23.15 percent ; the right-of-center Republicans 46 seats with 1.4 million — 5.41 percent. 

In other words, it took 70 629 votes, on average, to get one National Rally member of the National Assembly elected; 38 461 for one New Popular Front member; 37,500 for a Macronist; and 30,434 votes only for a Republican.

That may lack for logic, but that’s the name of the game in a two-round majority ballot, a Gallic modified form of the Anglo-Saxon first-past-the-post system. As long, though, as you don’t really pay attention to the popular vote figures. 

In America, the discrepancy between popular vote and seats surfaces only in — apart from the United States Senate — presidential elections when a nation-wide popular vote majority doesn’t translate to a majority in the Electoral College. The aggrieved party will talk for a while about abolishing the College. Until pundits will point to a possible revenge under the old unfair system in the next presidential election.

In France, however, such a discrepancy cannot go unnoticed, since many elections, outside the legislative ballots, are based on proportional representation in one way or another. That’s the case with the nation-wide direct presidential election, the regional elections, many of the local elections, and finally the European Parliament elections. The French are thus torn between two parallel, competing legitimacies. This is perhaps the main reason why they are losing faith in their democracy.

Naturally, trained observers knew all along that the National Rally’s impressive returns in the proportional European Parliament ballot on June 9 and even in the general election’s first round on June 30 would not translate easily to a parliamentary majority. The Rally was in need of further allies and could find none.

On the contrary, the left and the Macronists were able to engage in ubiquitous if unnatural crossed alliances so as to reinforce each other and split the spoils between themselves. At Avignon, the Macronists did not interfere in the election of Raphael Arnault, a left-winger on police records for organized violence and antisemitic aggression. 

In return, the far left allowed a former Macronist prime minister, Elisabeth Borne, to be reelected in Normandy. Mme. Borne was the driving force behind a comprehensive pensions’ reform that the far left has sworn to scrap as soon as possible. For all that, neither the left nor the Macronists achieved what would pass as a decent relative majority, not to mention an absolute majority. Thus, they are arithmetically bound to stay together.

The most obvious solution would be to set up a Macronist-led but liberal-leaning coalition. On paper, a 314-seat majority can be secured if the Macronists, the Republicans and 100 New Popular Front parliamentarians agree to work together. That would be well above the 289-seat absolute majority.

Mr. Macron would certainly agree to nominate a prime minister from the moderate left to that end: for instance a member of the rump socialist party.  The socialist predecessor of Mr. Macron as president, François Hollande, has just been elected in southwest France and seems to be prepared to take over the job.

The problem is that neither the Republicans nor the left-wingers are willing to renounce essential tenets of their respective platforms in the process. Take pension reform for example. It was originally the Republicans’ brainchild. On the other hand, fighting the reform was for years the hallmark of the left.

It is not just a matter of doctrine. It is an electoral issue. If the Republicans surrender here, they will lose their last supporters and vanish as a party. If the moderate left surrenders, it will be branded as treacherous by the extreme left — Jean-Luc Mélenchon’s France Unbowed party — and lose their own voters.

This is all the more so relevant since it is widely believed that the present National Assembly will last one year only, until Mr. Macron would be allowed, under the constitution, to call a new snap election.

However, some French politicians seem to be already thinking out of the box. The charismatic 35 years old former minister of Education, Gabriel Attal, who had been appointed prime minister on January 9, resigned yesterday after the completion of the ballot, while emphasizing — as is customary — that he would remain in office as long as necessary, that is, until the day after the Olympic Games. Mr. Macron, no less customary, asked him to stay “for the moment.”

Remarkably enough, though, Mr. Attal started his public resignation statement with a phrase — “My dear compatriots” — that had been used until now by the National Rally’s co-leader, Jordan Bardella, alongside Marine Le Pen. Mr. Attal then referred to the dissolution of the Assembly by Mr. Macron as something “he did not wish for.”

Finally, he cryptically mentioned “a new political supply.” Does it mean Mr. Attal envisions launching a new movement in the future, out of the ruins of Macronism? And that he has already started to court the National Rally constituency?