“It is now essentially a Macron-Le Pen government,” said Mr Mélenchon, referring to the leader of the far-right National Rally (RN).
He then urged people to join left-wing protests against President Macron's decision planned for Saturday.
Mr Barnier needs the support of 289 of the 577 lawmakers to survive a vote of confidence.
Marine Le Pen has made it clear that her party will not join his administration, but she appears to have met at least one of the National Rally's initial demands: that she be someone who “respects other political forces.”
Jordan Bardella, the 28-year-old president of the Council of State, said Mr Barnier would be judged on his words, his actions and his decisions regarding France's next budget, which must be submitted to parliament by October 1.
He cited the cost of living, security and immigration as the main emergencies for the French people, adding that “all political means are being reserved in case these problems are not resolved in the coming weeks.”
