“This is now essentially a Macron-Le Pen government,” said Mr Mélenchon, referring to the leader of the far-right National Rally (RN).
He then called for people to join a left-wing protest against Mr Macron’s decision planned for Saturday.
To survive a vote of confidence, Mr Barnier will need to persuade 289 MPs in the 577-seat National Assembly to back his government.
Marine Le Pen has made clear her party will not take part in his administration, but she said he at least appeared to meet National Rally’s initial requirement, as someone who “respected different political forces”.
Jordan Bardella, the 28-year-old president of the RN, said Mr Barnier would be judged on his words, his actions and his decisions on France’s next budget, which has to be put before parliament by 1 October.
He cited the cost of living, security and immigration as major emergencies for the French people, adding that “we hold all means of political action in reserve if this is not the case in the coming weeks”.
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