Leaders of the New Popular Front (NFP) angrily condemned Mr Macron’s refusal to select their candidate.
Marine Tondelier, the leader of the Greens, said that the president’s actions were a “disgrace” and a “dangerous democratic irresponsibility”.
François Ruffin, a former member of the hard-Left France Unbowed, said: “The madman at the Elysée dissolves the Assembly on a whim, then sits on the results of the elections. The people must reject Macron, in the name of democracy. He is the cause of chaos and instability.”
Ms Castets, a little-known senior civil servant and economist chosen among the hastily cobbled Leftist alliance after weeks of deliberation, also hit out at Mr Macron.
“Democracy means nothing to the president,” she said in an interview with France Inter on Tuesday. “We are faced with a president of the Republic who wants to be president of the Republic, prime minister and party leader at the same time.”
France Unbowed announced that it will be submitting a motion to impeach Mr Macron in the National Assembly. Any proposal for prime minister other than Ms Castets would also be subject to a motion of no confidence, the party added.
“The gravity of the moment calls for a firm response from French society against the incredible abuse of autocratic power of which it is the victim,” a statement from the LFI said.
The party also called for marches and protests in order to force the president to recognise the results of the election.
But the outgoing interior minister Gérald Darmanin defended Mr Macron, calling his move practical and necessary.
“The New Popular Front government has no chance of prospering for more than a day,” Mr Darmanin said during an interview with the news channel BFMTV.
“All political parties that do not belong to the New Popular Front has that it will censure it the same day the government is appointed.
The president said he will begin a fresh round of consultations with party leaders starting on Tuesday. The NFP has indicated it will not return to the Elysée unless it’s to discuss the appointment of Ms Castets.