With a week until the first round of voting, support for veteran La France Insoumise candidate is rising in a four-way contest

Will the real Jean-Luc Mélenchon stand up? On Tuesday, Mélenchon, the rising star of the French presidential election, will appear in the eastern city of Dijon. Simultaneously a 3D hologram of the veteran hard-left politician will be beamed to six other French cities. He may not literally be there, but just days from France’s heavily contested leadership vote “JLM” will be attempting to show that his programme has more substance than his ethereal appearance might suggest.

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In an election where historic and “never before” moments have become commonplace, the spectacular rise of Mélenchon has crossed a new line. Pollsters agree he is now a serious challenger to Les Républicains candidate François Fillon, who is in third position. Whether he can go further is anyone’s guess.

The favourites to make the second-round runoff on 7 May remain far-right Front National candidate Marine Le Pen and the independent centrist Emmanuel Macron. But with up to one-third of France’s 47 million voters undecided, and another 30% so disillusioned with French politics that they say they will abstain, the field is still wide open.

Two months ago any suggestion that Mélenchon, head of La France Insoumise (Unbowed France), could be a serious contender for the Elysée would have been thought laughable. Now it is no joke. Mélenchon’s popularity is running level with the beleaguered, scandal-hit Fillon in some polls, higher in others.

Le Monde says France is in the unusual situation of having four presidential candidates, any one of whom could win. Like Le Pen, Mélenchon is appealing to young voters with his hologram meetings, his upbeat election messages and his entertainingly forthright approach to televised debates.

Les Echos, France’s financial newspaper, described Mélenchon as “the new French risk”. Mélenchon would dramatically raise public spending, partly through taxing salaries above €400,000 (£339,000) at 90%. He wants to renegotiate EU treaties and quit Nato, the World Trade Organisation, the International Monetary Fund and the World Bank, all of which are viewed by La France Insoumise as instruments of a failing globalised capitalism.

The candidate responded in typical style last week to dire warnings of what voting for him might mean. “Once again, they are announcing that my election win will set off a nuclear winter, a plague of frogs, Red Army tanks and a landing of Venezuelans,” Mélenchon blogged.

Mélenchon has been here before. In 2012 he was polling third with 17% two weeks before the first-round vote. In the end he finished with 11.1% of the vote.

Manuel Bompard, Mélenchon’s campaign chief, told the Observer he was “very optimistic” this time around. “We see that all scenarios are possible for the second round. We’ve been working on our campaign for 14 months and we are now reaping the benefits. It’s a troubling period for France, and people want to hang on to something solid in a storm. That is Jean-Luc Mélenchon’s main appeal.” Bompard dismissed the idea of a “useful vote”, where voters choose a candidate more for the long-term result – in this case, seeing off Le Pen – than personal political convictions. He says there is nothing to fear with Mélenchon except fear itself. “I don’t believe in the tactical vote: people should follow their hearts and their convictions. The situation in the country is not very reassuring already, so what is there to fear with Jean-Luc Mélenchon? He is proposing a reasonable response to the country’s problems.”

Bompard denied that Mélenchon was scaring voters with his anti-Europe rhetoric. “We are very attached to the European project. But we all know, and we have seen from elsewhere in Europe, that people want the EU to change. If we continue on the road we are on now, and if we don’t act determinedly, we will kill off this ideal.”

Moroccan-born Mélenchon is a divorced father of one, who refuses to discuss any aspect of his private life. His parents split up and he moved to Normandy when he was 11. He later studied philosophy, and was a Trotskyist student activist before working as a French teacher and a journalist. He signed up to the Socialist party in the 1970s and was elected to the Senate in 1986, becoming the youngest member of the upper house. Marie-Cécile Naves, a political and policy analyst, said Mélenchon portrays himself as an outsider but is in fact more than familiar with France’s corridors of power.

“Jean-Luc Mélenchon is a veteran of French politics; he’s been around a while, he has been a minister and a European MP, but he is forging this image as a revolutionary. He says what he wants, he’s an excellent speaker, and in the end he has nothing to lose. Does he really want to rule the country? That’s another question,” Naves said. “Mélenchon appeals to a certain kind of voter who is angry at Europe, at the banking system, at inequalities, and wants to upset the apple cart.”

Naves said that, with four frontrunners, the election was extremely hard to predict. Pascal Perrineau, president of Sciences Po’s political research institute Cevipof, agrees. He refused to be drawn on what might happen next Sunday, saying the campaign was too volatile.

“Never forget the French are a people who cut off heads. We did this. Literally,” Perrineau said.

POLICY DIFFERENCES

Marine Le Pen

Hold an in-out referendum on EU membership. Leave the Schengen passport-free area and the euro. Make employers who hire foreigners, including EU citizens, pay an extra tax of 10% of the employee’s salary. Reduce income tax for the lowest earners. Reduce the level of legal immigration to 10,000 people a year.

Jean-Luc Mélenchon

Renegotiate the EU treaties and put these to a referendum. Raise the minimum wage and civil servants’ salaries. Limit fat-cat pay by fixing maximum salaries, with 90% tax on earnings more than €400,000.

François Fillon

Reform the Schengen agreement to tighten control of the EU’s external borders. Slash 500,000 public sector jobs in five years, cut public spending, reduce taxes and break the power of the trade unions. Cut immigration to a “strict minimum” through the use of quotas.

Emmanuel Macron

More flexibility on labour laws and a loosening of the 35-hour week. Cut public spending by €60bn and scrap 120,000 public sector jobs by 2022. Cut the number of MPs. Maintain the Schengen travel area.

Benoît Hamon

Universal basic income, initially for low-paid workers and students. Five-year investment plan worth €100bn for urban and environmental renovation. A tax on banks’ “super-profits”. In Europe, switch emphasis from the free market to greater social protection.. Set up a new “humanitarian visa” system for refugees.

• This article was amended on 16 April 2017. In an earlier version we incorrectly attributed comments by Marie-Cécile Naves to another analyst, Virginie Martin. This has been corrected.