In the past the dilemma was confined to the right. RN was regarded as beyond the pale, so the centre-right faced hell and damnation on the few occasions it joined them in a tacit arrangement to keep out the left.

But this year, the ostracism of the far-left LFI is a new feature of French politics.

Under its leader, Jean-Luc Mélenchon, LFI formed an alliance with the PS, Greens and Communists to give the left a strong showing in the last legislative election in 2024.

But since then, the pact has unravelled. For many LFI opponents, the last straw was the murder of a far-right student in Lyon last month, allegedly by a far-left gang containing an LFI parliamentary assistant.

And then came what was interpreted as antisemitic joking by Mélenchon when in a speech he played with the pronunciation of Jeffrey Epstein – the disgraced, late US financier and sex-offender – apparently to emphasise the name’s Jewishness.

All this makes impossible any formal alliance with LFI, which is why on Sunday evening PS leader Olivier Faure ruled out any “national” accord to join forces in next Sunday’s second round.

Significantly though, Faure did not rule out “local” arrangements with LFI. And already in Toulouse the PS and LFI have announced they are merging their two lists in order to defeat the incumbent right-winger.

For the right, this all reeks of hypocrisy – and in the coming days the airwaves will be loud with cries of leftwing “double standards”.

To which the left will reply: “Clean out your own house and stop flirting with Fascists!”

If it sounds polarised, ill-tempered and fractious, that is because it is.

In France as elsewhere, politics is more and more determined by what happens on the outer fringes.

If it is true of these municipal elections, how much truer it will be in next year’s presidentials.