How do they work and why are they so significant?

Emmanuel Macron’s decision to call two rounds of elections on 30 June and 7 July is seen by rivals and allies as a reckless gamble that could hand political power to the far right.

He wants to regain control of French politics, but that’s not what the opinion polls say will happen.

An hour after the far-right National Rally party of Jordan Bardella and Marine Le Pen trounced Emmanuel Macron’s Renew alliance in European elections, the French president went on TV to say he couldn’t act as if nothing had happened.

After National Rally had scored 31.4% of the vote to his party’s 14.6%, he said it was time for France’s people and politicians “who do not recognise themselves in the extremist fever” to build a new coalition.

Mr Macron had no need to call National Assembly elections as they were last held in June 2022 and no further vote was due until 2027. He has since insisted it was the “most responsible solution”.

Apparently Mr Macron had been thinking about calling an election for months, but France is busy gearing up for the Paris Olympics from 26 July to 11 August.

He clearly wanted to break a logjam, after his failure to secure an absolute majority in the National Assembly in June 2022. Passing laws has become a real headache – he had to force through pension reforms without a vote while tougher immigration rules required National Rally support.

“France needs a clear majority if it is to act in serenity and harmony,” Mr Macron argues. And yet he has left French politics in turmoil.

His centrist alliance of Renaissance, Horizons and MoDem is languishing in third place and his hopes of attracting the centre left have foundered.

The Socialists have formed a New Popular Front with the Greens, far-left France Unbowed (LFI) and Communists.

“This decision has created everywhere in our country, in the French people, worry, incomprehension, sometimes anger,” says Finance Minister Bruno Le Maire.

National Rally could win power in France for the first time. It is led by 28-year-old Jordan Bardella and in parliament by Marine Le Pen, who has fought for the presidency three times and lost each time.

But each time she won more votes. Now the polls says her party could become the biggest in France, falling short of an absolute majority. Not far behind in the polls is a broad left-wing alliance, and they include parties on the far left.

There are 577 seats in the National Assembly, including 13 overseas districts and 11 constituencies that represent French expats abroad. For an absolute majority a party needs 289.

The Macron alliance had only 250 seats in the outgoing Assembly and had to build support from other parties every time to pass a law.

The first round eliminates all candidates who fail to make 12.5% of the vote. Anyone who scores 50% of the vote with a turnout of at least a quarter of the local electorate wins automatically. That happens in a handful of constituencies.

The second round is a series of run-offs fought either by two, three or sometimes four candidates. Some candidates may drop out before 7 July to give an ally a better chance of stopping a rival from winning, for example from the far right.

The two-round system means nothing is clear-cut.

Even if National Rally qualifies for the second round in a large number of constituencies, voters could choose to adopt “le vote utile” – tactical voting – to keep the party out.

They have 88 seats in the outgoing parliament, but polls suggest they could go well above 200.

Aside from opinion polls, all we have to go on is the European election result which gave National Rally 31.37% of the vote and the other far-right party Reconquête 5.47%. Some supporters of the centre-right Republicans may back RN, but equally others may join the movement to block them – to form a “barrage”.

The combined vote of the left, Greens and far left was above 30% too. But not all left-wing voters will back the New Popular Front because of the involvement of Jean-Luc Mélenchon’s far-left France Unbowed (LFI).

Another factor is turnout, which will be considerably higher than the 51% in the 9 June European Parliament vote.

Whoever wins, Mr Macron has said he will not resign as president.

If his party loses, and either National Rally or the New Popular Front win, that leaves almost three years of “cohabitation”, or power-sharing, when the president of one party heads the state and another party runs the government.

It’s happened before, with domestic policy in the hands of the prime minister and cabinet and foreign and defence policy in the hands of the president.

Not necessarily. Mr Macron decides who will lead the next government, according to the constitution. But he does have to reflect the make-up of the new Assembly, so if National Rally are the predominant party he could find it hard to choose someone else.

And if RN wins an absolute majority, Jordan Bardella would be the obvious choice as nominated by the party itself. RN campaign posters proclaim him as prime minister, at 28 he is a big presence on TikTok and he has been a member of the European Parliament since 2019.

But Mr Bardella has himself ruled out becoming prime minister if RN doesn’t secure that absolute majority: “I don’t want to be the president’s assistant.”

A relative majority, he said would leave him unable to act: “I’m not going to sell the French people measures or actions that I couldn’t follow through.”

Not for more than 20 years, as parliamentary elections now come hard on the heels of presidential votes, and voting preferences do not change much within that time.

There have been three periods of cohabitation in the past:

1997-2002 Socialist Lionel Jospin was prime minister under centre-right President Jacques Chirac

1993-95 Centre-right Prime Minister Edouard Balladour worked with Socialist President François Mitterrand during his second term

1986-88 Jacques Chirac was prime minister under President François Mitterrand

But nothing has really prepared France for the kind of cohabitation that could occur after 7 July, with either the far right or elements of the far left trying to get along with a centrist president.

For years Marine Le Pen has sought to “de-diabolise” or detoxify her party from the antisemitic and extremist roots of her father, Jean-Marie Le Pen, and his fellow founders of the National Front, which she renamed as National Rally.

However, its strict anti-immigration policies remain and a ruling earlier this year by the Council of State, France’s highest court for administration, confirmed it could be considered “extreme right”.

France football captain Kylian Mbappé has warned his compatriots “the extremes are at the gates of power” and that France is “at a very important moment of history for our country”. Jordan Bardella swiftly hit back, criticising multimillionaire “sports figures giving lessons to people struggling to make ends meet”.

The RN has long called for a ban on Muslim headscarves in public, although Mr Bardella has now said this would not be a priority until the next presidential election.

National Rally has taken money from Russia and Marine Le Pen has been pro-Kremlin, anti-Nato and anti-EU. And yet many of their extreme positions on leaving Nato’s integrated command and increasing ties with Russia have been quietly dropped.

Leaving the EU has not been on the agenda since 2022. Instead, Mr Bardella focuses on cutting VAT (sales tax) on energy and a list of 100 essential goods and repealing the Macron pension reforms in a matter of months.

The New Popular Front is an unlikely alliance of Socialists, Greens, Communists and France Unbowed.

They have promised to scrap the Macron pension and immigration reforms and their platform is otherwise based on the idea that “it’s either the far right, or us”.

President Macron has attacked the group as being “totally immigrationist” and allowing people to change gender at their town hall, an accusation that has prompted allegations of transphobia.

The Popular Front has promised to fight antisemitism, even though it includes far-left candidates who have been accused of making antisemitic remarks.