Who is he?
He's a 65-year-old veteran politician who quit the Socialist party after 30 years in 2008 and is now head of his own movement "La France Insoumise" (Unbowed France).
Long known for being aggressive and acid-tongued, he has toned down his rhetoric for this campaign but is still able to deliver a zinger or a witty putdown when required.
"I'm becoming a reassuring figure," the divorced father-of-one told the Journal du Dimanche on April 2. "I'm less of a hothead."
After refusing an alliance with Socialist candidate Benoit Hamon, he appears now to have eclipsed him as the main voice on the left.
"He invented political stand-up. He's become a showman," according to a former colleague in the Socialist party Julien Dray.
Melenchon ran for president in 2012 and won 11.1 percent of the vote, lower than polls had forecast.
Watch: France election candidates go head-to-head in TV debate
Why so popular?
His climb appears linked to strong performances in two televised debates on March 20 and last Tuesday during which he delivered some memorable soundbites, particularly when clashing with far-right leader Marine Le Pen.
"Leave us alone with your religion!" he shouted at her last week at one point.
In an election marked by high levels of anger and people wanting to kick out the established political class, he has emerged as a charismatic alternative to Le Pen and the other "outsider", pro-business independent Emmanuel Macron.
From the beginning of the campaign, he has also built up a loyal core of supporters on Twitter and via his own YouTube channel -- a way for him to circumvent the traditional media, which he accuses of being biased.
In a sign of nervousness, Macron supporters spread an online video over the weekend highlighting Melenchon's tax plans while party secretary general Richard Ferrand urged voters to delve into his radical programme.
How leftwing is he?
He's backed by the French Communist Party, is an admirer of late Venezuelan president Hugo Chavez and has a huge tax-and-spend economic programme.
He wants to reduce France's working week to 32 hours from its current 35 hours and lower the retirement age back to 60.
He proposes increases in the minimum wage and social security payments paid for in part by greater taxation of the rich. Any earnings beyond 33,000 euros a month would be taxed at 100 percent.
He wants to quit nuclear power, which produces around 75 percent of France's electricity, and renationalise the partly-privatised national power group EDF.
In foreign affairs, he wants to pull France out of the market-friendly European Union as well as the Western military alliance NATO, and he has supported Russia's military action in Syria and Ukraine.
He has also compared German Chancellor Angela Merkel, current President Francois Hollande's closest ally, to war-mongering Prussian statesman Otto von Bismarck.
"I'm the candidate for peace," he said on Sunday with an olive branch in his jacket pocket.
One of his signature domestic proposals is constitutional reform. He wants to scrap the existing powerful executive presidency and return France to a parliamentary system.
He wants to legalise cannabis and welcomes immigration.
"Today as yesterday, I am delighted that France is a mix of races and all the children are our children," he said on Sunday.