France’s hostage nightmare
Flags will be at half-mast for three days from Friday, after the murder in Algeria of hostage Herve Gourdel.
The gesture - ordered by President Francois Hollande - shows how this killing marks new ground in the war against jihadism.
There have been previous murders of French hostages in north and east Africa. Since 2010, nine have been killed by Islamists in Mali and Somalia.
But Herve Gourdel's is the most disturbing.
Partly that is because of the manner of his death: the cold-blooded beheading staged for the camera.
And partly it is because it feels like a step in a terrible chain of events, leading inexorably from horror to horror.
Struggling to comprehend
Across France, if one discounts the predictable pronouncements from officialdom, the reaction has been mostly one of numbed silence.
Even in Saint-Martin-Vesubie, the mountain village near Nice where Herve Gourdel lived, local people have reacted to journalists' questions in monosyllables.
They are not being rude. They just do not know how to express their horror and anger.
After the first French air raids on Islamic State (IS) a week ago - and then the group's explicit threat to target French nationals - the possibility that the war could move closer to home became suddenly tangible.
On Tuesday, the government issued a warning to the French - especially those living abroad - to be on their guard.
And then on Wednesday, Herve Gourdel was beheaded. Events moved so quickly that people are struggling to comprehend what it means.
For many in France, the murder is all the more shocking because Herve Gourdel was precisely the kind of person that they instinctively admire.
With his craggy, outdoor-philosopher looks; his independence; his love of mountains and photography; his love of travel and openness to other cultures; his attachment to roots and family - he represented a kind of idealised self-image for the French.
'Assault on values'
Journalists - who saw the original video in which he announced his capture - say he spoke with a quite uncanny calm, another cause for respect.
As President Hollande said, Herve Gourdel was killed for no other reason than that he was French.
And the French will see his death - more clearly perhaps than those of previous hostages - as a direct assault on the values they hold dear.
In Paris, the president has now called for security to be boosted on public transport and in public buildings.
The Vigipirate patrol system remains at its second-highest level, and soldiers are more visible around tourist spots and railway stations.
There is no outward display of fear. But deep down everyone knows France is entering a period of nervous uncertainty such as has not been seen for many years.
Britain is exposed in the same way, of course. It, too, is in the fight against Islamic State (though it has yet to launch air strikes) and it, too, has nationals who have joined the jihad.
But France feels in the grip of the unknown. The Middle East and North Africa have never felt so dangerous. And they have never felt so close.