Technically there is no candidacy, the french president appoints whoever they want as prime minister, but it’s been “common use” to name someone associated with the main party represented in the parliament

The divided NFP alliance has been arguing over who to put forward as their joint candidate for prime minister. For two weeks, internal conflicts – notably between LFI and the more moderate Socialists – thwarted efforts to find a figure who would be able to prevail over a vote of no confidence in the Assemblée.

Left-wingers will forever be their own worst enemy. Even after showing that unity can be a win, they will continue to squabble.