In Fiscal Kombat the player roams the streets pretending to be Mr Melenchon as he battles against oligarchs and rival politicians.
The aim is to shake money from the rich to pay for Melenchon's policies.
The player's challenge is to get as much money as possible while avoiding the attempts of the rich to maul him to death.
Among the series of "bosses" that Melenchon must take on are former president Nicolas Sarkozy; the head of the IMF, Christine Lagarde; the tax-evading politician Jerome Cahuzac; and the L'Oreal heiress Liliane Bettencourt.
French election 2017: Who are the candidates?
Presidential rivals Emmanuel Macron and Francois Fillon must also be defeated.
According to Le Monde, the game was created by Melenchon supporters who met on the 18-25 chatroom of Jeuxvideo.com, a French gaming website.
It has since been fully embraced by the candidate himself, who has released a YouTube video of him playing the game.
"The hero of the game, it's me. I and the people playing my character fighting the oligarchs," Melenchon says in the video.
During one of the game's levels, Melenchon teleports away from an exploding nuclear power station.
That is a reference to him giving a speech via hologram earlier this year.
Who is Jean-Luc Melenchon?
Mr Melenchon is a veteran of French left-wing politics.
He left the socialist party in 2008 to found the Left Party.
Backed by France's Communist Party, he says the means of production, trade and consumption must be changed, and cites climate change as one of his concerns.
This is not the first time he has stood for the presidency.
In 2012 he received 11.10% in the first round.
He is not a favourite to win the election but has recently risen in the polls.
There are 11 candidates in total for the French Presidency.
The first round of voting will be on the 23 April with the final round on the 7 May.
Supporters of the far-left French presidential candidate Jean-Luc Melenchon have created a video game where players bash the rich.