Two terrorists entered a village church in Normandy at morning Mass on Tuesday, slit the throat of an elderly priest and critically wounded another person before police shot the pair dead. Islamic State claimed credit, adding to a list of recent atrocities that includes a suicide bombing and knife attack in Germany and the Bastille Day murder of 84 people in Nice. President François Hollande says France is at “war” with Islamic State, and we’d like to believe he means it.

Mr. Hollande has been sounding the war theme since November’s terror attacks in Paris, and to that end French planes have been dropping bombs on Islamic State targets in Syria and Iraq. The President has also approved a modest increase in defense spending, again extended a state of emergency, and is considering measures to improve intelligence gathering and interagency coordination, along the lines of the U.S. National Counterterrorism Center.

All of this is helpful at the margin. Yet France had a robust intelligence service long before the rise of Islamic State. The Normandy church was mentioned on an Islamic State hit list discovered by authorities last year, and one of the attackers seems to have been on bail and under electronic surveillance for seeking to go to Syria.

All this proves again that a war on terror can’t be won merely with better police work or the “intelligence surge” proposed in the U.S. by Hillary Clinton and Donald Trump. Proper surveillance of a single suspect requires 20 or so agents, which means France would need some 200,000 officers to monitor the people already on the government’s terror list before November’s attacks. The real number of French jihadists has surely grown.

The proper response to Islamic State is to go on swift and decisive offense, beginning with the eradication of its strongholds in Syria, Iraq and Libya. Mr. Hollande may have declared war on Islamic State, but so far the fight has been more symbolic than strategic. Unless that changes, Tuesday’s attack in Normandy will merely be one more of many horrors to come.