But while commentators worldwide have focused on the steady rise of the far-right, fiercely anti-immigrant National Front of Marine Le Pen, few have paid any attention to the leftist fringe.
Mélenchon has vaulted into the picture in the past week and shares with Le Pen the desire to drastically alter France's relationship with the EU, the 28-state bloc it once designed.
Mélenchon is running as the candidate of the Unbowed France political movement, in an alliance with the French Communist Party.
The latest polls show him narrowly trailing Emmanuel Macron, long seen as the favourite, and Le Pen, expected to qualify for the final round of the two-round vote but to lose to Macron in the final.
In the final days of a truly unprecedented campaign, Mélenchon's unexpected surge is a reminder that radical change is in the air, and that its extremist apostles - right or left - may soon hold power.
Some have reacted with panic: Investors have begun frantically selling off French bonds, while the head of France's largest trade union has decried what he described as Mélenchon's "rather totalitarian vision".
But thousands of others have responded with joy.
Nearly 25,000 people assembled in the predominantly middle-class northern French city of Lille to hear Mélenchon, dressed in his signature Mao jacket, take the stage.
With his distinct wit, erudition and rhetorical flair, he charmed his crowd, packed inside and outside a local sports arena, waving communist banners, Palestinian flags and signs adorned with the Greek letter "Phi," the campaign's official symbol.
"It's the people who make history," Mélenchon said, standing on a dais before thousands. "It's you! So we have to do it. Let's go, folks! Courage!"
Perhaps more than any of the other candidates, it is Mélenchon who best represents 2017's potential rupture with history, or at least the status quo.
Central to his platform is the promise to abolish France's Fifth Republic, the system of Government established by Charles de Gaulle in 1958.
What Mélenchon detests in this style of government is its monarchical presidency - designed for de Gaulle himself - which can dissolve Parliament at will and has few checks and balances on its power.
Mélenchon has pledged to found what he calls the "Sixth Republic," a vision that would "take us out of this presidential regime, notably with proportionality in all elections."
It is an idea that resonates widely - even among those who do not necessarily support Mélenchon's other more radical proposals, including taking France out of Nato and imposing a 100 per cent tax on all income earned over €400,000.
"He's the only one who dares to say it, but there are so many others who agree with that," said Jacques Bruley, 25, an engineer with Lille's tram system.
Bruley said he was not a full Mélenchon supporter and had not yet decided whether he would vote for him, but that this particular idea was an imperative.
"There's one person who holds an unconscionable amount of power. It's wild," he said of the presidency. "And when you talk about 'change,' it's Mélenchon who would really bring that kind of big change."
The reality is that "big change" is likely to come, with or without Mélenchon.
For the first time in the history of the Fifth Republic, neither the Socialists nor the Republicans - the vaguely centre-left and centre-right parties, respectively, that have governed France since 1958 - are likely to triumph at the ballot box.
The contest will probably be a face-off between two political outsiders: the independent Macron, the far-right Le Pen, and, possibly, the communist Mélanchon.
Despite their ideological opposition, there are certain similarities between the platforms of Le Pen and Mélenchon.
Both favour versions of economic protectionism to bolster a strong French state, and both would ultimately like to see France exit the EU - albeit for difference reasons. Le Pen sees Europe as a threat to France's sovereignty and national identity. Mélenchon views Europe as an oppressive neo-liberal regime that has forgotten the poorest members of society.
He proposes renegotiating France's membership in the bloc, and if things don't go his way, leaving altogether.
But many Mélenchon supporters do not recognise the similarity.
"I don't like the comparison," said Alexi Descamps, 25, an IT engineer in Lille. "[Le Pen] has a very aggressive politics on immigration, and he doesn't. He's extreme left, and that's what we need - he's the only one who proposes a departure from capitalism."
In a shocking turn of events, Mélenchon is in third place - behind Macron and Le Pen but ahead of François Fillon, the centrist conservative whose campaign has suffered in the wake of a public spending scandal.
If Mélenchon does not qualify for the second and final round, which polls still suggest he will not, his supporters said they were not sure who they would support instead - or even if they would vote at all.
"Of course I will vote for whomever is not the extreme right," said Eva Alain, 20, an audiovisual student. "But if it's Fillon, it's impossible, and if it's Macron, it's difficult."
In recent months, Mélenchon - once a distant afterthought in the constant election predictions - has presided over a digital campaign that has successfully appealed to a wider base of voters, especially among the young.
He has more YouTube followers than all of his principal opponents combined.
He released an online video game titled "Fiscal Kombat," in which players attack bankers and, at a higher level, Christine Lagarde, the French director of the International Monetary Fund, in the name of redistributing wealth to the masses.
Even so, if young people in France affiliate with a party, it is generally the party of abstention. According to a recent poll from the Ifop agency, the intent to abstain has risen to 52 per cent among voters ages 18 to 25.
In the final days of the campaign, the field is wide open.
