Branding himself “the sound and the fury” after the William Faulkner novel of the same name, the Communist-backed former Trotskyist is shaking up the campaign with his fiery oratory and revolutionary call to arms.
The latest opinion polls show him storming into third place in voting intentions for the 22 April first round, still well behind conservative president Nicolas Sarkozy and Socialist François Hollande, but overtaking far-right candidate Marine Le Pen, his bitter rival for working class votes.
Opinion polls now credit Mr Mélenchon, 60, with up to 15 per cent of the vote, more than twice what he commanded in January. He has vacuumed up most of the protest vote previously split among Trotskyist, Communist, left-sovereignist and Green candidates.
He staged another show of force in Toulouse last Thursday, drawing tens of thousands to a rally in the central Place du Capitole at which he called for France to reassert its sovereignty and withdraw from Nato.
“When there is no more liberty, civil insurrection becomes a sacred duty of the Republic,” Mr Mélenchon declared, to cheers from supporters waving red flags.
In March, he drew an even bigger crowd for a march to the Place de la Bastille in Paris, symbolically re-enacting the capture of the ancien régime fortress that was a high point of the 1789 French Revolution.
His platform promises to raise the minimum wage to €1,700 (£1,400) a month, cap incomes at €360,000 a year, confiscating anything above that limit, reinstate retirement at 60 for all and ban profitable companies from laying off workers.
So far, analysts reckon he has done Mr Hollande a favour by mobilising people who might have stayed home or voted for Ms Le Pen. Polls show 70-90 per cent of Mélenchon supporters intend to vote for Mr Hollande in the run-off.
But if he gets too big a score, it could scare middle-class and centrist voters into backing Mr Sarkozy in the decisive ballot. The president has begun to warn voters that Mr Hollande would be a “hostage to Mélenchon”.
Mr Mélenchon’s spokeswoman, Clémentine Autain, has made it clear his party would seek both policy concessions and Cabinet seats, saying: “We would like to see the political conditions emerge for us to take part in a government.”
Mélenchon, a former senator and MEP, was minister for vocational training under Socialist prime minister Lionel Jospin from 2000 to 2002, but relishes being an outsider.
A child of the 1968 student-worker uprising, he makes no apologies for his straight talk and independent spirit, which in the past have seen him expelled from the Internationalist Communist Organisation, quit the Socialists, and eventually form his own more radical movement, the Left Party.
He plays on fears of unbridled globalisation undercutting French workers’ living standards, and on hostility to the European Union’s free market policies.
He was one of the leaders of the “No” campaign in a 2005 French referendum that rejected an EU constitution and is now demanding a plebiscite on the treaty on budget discipline signed by EU leaders in March.
“I’ve got a strong temperament. What do you expect? You wouldn’t want a damp squib to face up to this kind of challenge,” he said in recent TV interview.
Of his private life, Mr Mélenchon shuns what he calls the personality cult that surrounds modern-day politicians.
An unauthorised biography, Mélenchon, the Plebeian, says he married in the 1970s, divorced in the mid-1990s and has one daughter, born in 1974, but his campaign team has refused to confirm any details unrelated to his political career.
Much of his attraction lies in his mastery of public oratory, honed during his time with the Communists, tempered with a judicious smattering of literary and historical reference and capped with a razor-sharp wit.
He derided Mr Hollande early in the campaign as a “pedal-boat captain”, suggesting he couldn’t be relied on in a storm.
He was accused of demagogy and populism after publishing a book in 2010 calling for a citizens’ revolution entitled Qu’ils s’en aillent tous (“Get rid of the lot of them”).