On Tuesday Sarkozy fired Nathalie Kosciusko-Morizet as one of the Republicans' vice-presidents because she had spoken out against his "neither/nor" line that opposes the party to both the FN and the Socialists.
Not for the first time, the Socialists proposed a "republican front" against the FN, which would have meant standing joint slates in the second round of the regional elections in regions where the far right could win.
The Republicans said no to that, so the Socialists stood down in two regions - Nord-Pas-de-Calais-Picardie and Provence-Alpes-Côte-d'Azur - leading to a victory for the Republicans and their centrist allies and no seats at all for themselves.
"If the voters had applied neither-no, our candidates would have been beaten," was the reaction of Kosciusko-Morizet, who is widely known by her initials NKM.
Sarkozy's response was to fire her, a move that inspired NKM, whose great-grandfather was a founder member of the French Communist Party, to declare that believing that purges strengthen a party is "an old Stalinist idea".
She has been replaced by Laurent Wauquiez, the 40-year-old former minister who led the party to victory in the Rhône-Alpes-Auvergne with a hard-right campaign that included calls for internment camps and a promise to instal security scanners at entrances to the region's schools following the November Paris attacks.
The region was the only one where the FN's vote was lower than its score in the 2012 presidential election.
But the men who led the Republicans in the regions where the Socialists stood down have also come out against the neither-nor line, as has former prime minister Jean-Pierre Raffarin, the only member of the party's executive apart from NKM to vote against it ahead of the poll.
Raffarin has gone further and called for a joint plan of the mainstream parties to fight unemployment, which he says is the principal factor in the FN's electoral rise, although he adds that the Socialists must break with the hard-left Left Front and left-wing dissidents within the party.
Xavier Bertrand and Christian Estrosi, the Republicans' leaders in the regions where the Socialists stood down, have both called for a change in line and promised to work with the left.
On Monday Bertrand warned of a "political catastrophe" if the party leaders do not "wake up", while Estrosi, who has been accused of adopting FN-style policies in the past, calling for a "new political model" to satisfy the French people who are "disgusted by political squabbling".
Such calls must be music to the ears of Socialist Prime Minister Manuel Valls who has called for the right and the left to "talk to each other" and told parliament on Tuesday that he was open to suggestions from the right on how to fight unemployment.
But his party's first secretary, Jean-Christophe Cambadélis, seems to be looking left.
He has revived calls for a "people's alliance" of the left, an idea also raised by former housing minister and Green party bigwig Cécile Duflot, who wants a bloc of her party, the Socialists and the Communists.