The grotesque murder of an elderly priest as he conducted morning mass in his church in a quiet suburb in Normandy shocked not only France but the whole world.

Leaders from Europe, the US and beyond voiced solidarity with a nation still reeling from from the Bastille Day attack in Nice, when a lorry was driven into celebrating crowds killing 84 people.

One of Fr Jacques Hamel's brutal killers has been named as Adel Kermiche, a 19-year-old who had twice tried to reach Syria to fight with Islamic State (IS) and who was wearing an electronic tag having been put on probation by the authorities.

The same group claimed responsibility for the Nice attack, declaring killer Mohamed Lahouaiej-Bouhlel, a Tunisian, "a soldier of the Islamic State".

Last November, IS gunmen and bombers launched co-ordinated attacks across Paris, which left 130 people dead, including 90 at the Bataclan nightclub.

In the day's before the priest's killers burst into the church of Saint-Etienne-du-Rouvray, in Rouen, Germany witnessed four violent incidents, two of which are linked to IS.

Amid tightened security everywhere, it feels as if war is being waged on Europe and France in particular.

But that is the wrong way to view these appalling crimes and President Francois Hollande's response, while understandable, is a serious miscalculation.

"We will win this war," he declared in the immediate aftermath of Fr Hamel's slaying, warning also "the war will be long".

He used the same language after the Bataclan attacks, speaking of "acts of war" against France. He promised then to battle IS "without a respite, without a truce".?

President Hollande is right to say democracy is under attack. He is wise to call for unity.

But to declare war is to play into the terrorists' hands. These cruel, callous attacks on innocent people are designed to be as horrific as possible. They are intended to shock, outrage – and provoke a ferocious reaction.

IS wants to provoke a war with the West that would feed and fuel its twisted aims.

We will defeat them not by falling into their trap but by ignoring it, by cherishing our democratic freedoms, celebrating our diversity and maintaining our way of life. Keeping calm and carrying on, in other words.

Heightened security is inevitable. We must be vigilant. Governments must support their security services and pursue programmes aimed at preventing radicalisation. But such talk of war is wrong approach.

It is a lesson we thought we had learned. President Bush coined the phrase "war on terror" within days of the 9/11 attacks in New York. It reflected the mood of public fury – but it was quickly found to be counterproductive.

The UK Government renounced the term a decade ago, deciding it was "unhelpful". President Obama never used it and, three years ago, officially ended the US's war on terror.

Resurrecting it now is a retrograde step. Europe is suffering. Families have been torn apart. Communities are grieving, angry and afraid.

But it is France's proud traditions of liberty and fraternity – concepts alien and threatening to the terrorists – that will ultimately prevail, not talk of war.