There has been a surge of support for Melenchon
According to polls, after doing well in the the two televised debates, Mr Melenchon's support is not far from the frontrunners Emmanuel Macron and Marine Le Pen.
He was once seen as a maverick candidate, but he is now being taken seriously for the first time.
Mr Melenchon is an outspoken critic of the European Union, which he claims has been corrupted with neoliberalism.
Macron is leading the polls with Le Pen
Who will be the next President of France?
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I’m becoming a reassuring figure
In his manifesto, he proposed to reform the bloc then holding a referendum to give French voters the choice to accept the reformed terms of the EU membership of to leave the union.
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He said: “I’m becoming a reassuring figure.
“I’m less of hothead.”
Marine Le Pen has enjoyed good ratings in the polls
The 65-year-old candidate, who quit the Socialist party after 30 years in 2008, was declared the winner of the second, 11-candidate TV debate.
The polls show that support for Melenchon, who leads his own party ‘Unsubmissive France’ is up to 17 per cent with Ifop and up to 16 per cent with Opinionway.
Centrist Emmanuel Macron and far-right Marine Le Pen each have around 24 per cent of support from voters.
Thousands of supporters attended Melenchon’s rally on Sunday.
He said: “I’m the candidate for peace.”
Mr Melenchon’s proposals include a billion pound plan and a reduction in the working week to 32 hours, overhauling the EU and pulling France out of NATO.
Mr Melenchon, who refused an alliance with Socialist candidate Benoit Hamon, is backed by the French Communist Party and he wants to reduce the retirement age to 60.
He has proposed an increase in the minimum wage and social security payments paid for by greater taxation of the rich.
Mr Melenchon only won 11.1 per cent of the vote when he ran for president in 2012.
The first round election is Sunday, April 23.