The NFP, particularly the hard-left France Unbowed (LFI), has demanded for their right to form a government. The party argued that since it won the most seats, it should pick the new prime minister. It has chosen Lucie Castets, 37, as its candidate.
However, Macron’s party, along with the conservatives and the far right, have promised to vote no confidence in a left-wing government.
Macron is the President, not the PM, so he doesn’t have to leave. Moreover, he’s the only one who can appoint a new PM, so all the NFP can do is put forward a candidate and hope His Majesty Macron deems him/her to be worthy. The whole situation is essentially a soft coup by Macron and his party, there’s no way around it