It was a horrible and horrifying scene on Friday the 13th in Paris, where seven apparently coordinated terrorist attacks killed 127 people or more. The attackers used grenades and Kalashnikovs; four suicide bombings have been reported.

Center stage for this well-planned assault appears to have been the Bataclan concert theater, where more than 100 people have died. One witness there, according to BFM television, claimed that he heard rounds of automatic rifle fire and someone shouting “Allahu akbar!” And French radio reported a shooter shouting, “This is for Syria.”

French President François Hollande has understandably declared a state of emergency, closing roads and firming up borders while deploying the French military internally. The sheer levels of coordination, sophistication, and determination—as well from sporadic eye witness accounts—indicates that Paris has succumbed to yet another jihadist attack. First accounts of these tragedies can be notoriously imprecise, but that is the working assumption I will use to make my comments below.

These attacks come on the heels of a symbolic international victory in the targeted killing of Mohammed Emwazi, or “Jihadi John,” and a tactical victory by the Kurds in Sinjar against the so-called Islamic State widely known as ISIS. But after what appears to be the most coordinated terror attack in France yet—coming close enough to President Hollande’s location that he had to be evacuated from a football game at the Stade de France—it would be fair to say that these much-lauded symbolic and tactical victories against ISIS have not only been overshadowed, but totally overcast.

“Jihadi John” was of great propaganda value to ISIS as an international symbol of terror, though he held little operational or command value to ISIS hierarchy. And though the terror group’s defeat at Sinjar at the hands of brave Kurdish fighters was real, ISIS’s recent ability to apparently strike in Egypt’s Sinai, Lebanon’s South Beirut, and now in Paris with devastating results demonstrates this group’s undeterred, relentless drive to export terror. They possess no shortage of zealous volunteers or of operational reach, to make this twisted fantasy a reality.

Too many times we have heard “mission accomplished” moments in the fight against jihadists. From Bush’s declaration that the Iraq War was over to the Obama administration’s long-held belief that—by killing Osama bin Laden—al Qaeda and jihadism had been defeated. The talk on Friday that the death of “Jihadi John” was some kind of symbolic victory was only the latest. So why does this keep happening, and on this scale?

The answer is not a comfortable one.

Jihadist terrorism is alive and kicking. And though we must continue to put terrorists on the back foot by targeting their leadership, we will never kill our way out of this phenomenon. In January 2013, after Bin Laden’s death but long before ISIS’s emergence, my counter-extremism organization Quilliam declared (to choruses of raised eyebrows at the time), “It’s a full blown jihadist-insurgency, stupid.” And no insurgency is sustainable, or even possible, without a level of residual support for its core ideological aims among the core communities from which it draws its fighters.

Jihadism has well and truly taken root among an entire generation of angry young Muslims. This is particularly the case in Europe, where thousands have left to join ISIS. This insurgency is incredibly hard to tackle, because its recruits remain invisible in our very own societies, born and raised among us, fluent in our languages and culture, but full of venom for everything they have been raised into.

Though London is by now well overdue a similar attack, a question that could legitimately be asked is why does France seem to be bearing the brunt of such coordinated jihadist terror, up until now most potently symbolized by the Charlie Hebdo attacks? Unfortunately for France, though not unique to it, between 5 and 10 percent of its population is Muslim. Real, serious problems with economic and social integration prevail in this group, fuelling resentment on a scale that baffles most expert policy makers. Even if hundreds, out of millions, take this resentment to its deadly conclusion, France has a huge problem on its hands, as we saw on Friday. But so do we all.

Recognizing this is not to stigmatize every European or Western Muslim—the vast majority of whom are not, of course, jihadists—but it means being realistic about exactly where the challenge is coming from, and what the challenge is called: Islamism. Up until now the bitter truth that our Muslim populations have been subjected to decades of sustained Islamist propaganda by those who live among them has gone almost totally ignored. The long term solution cannot continue to ignore this truth, and cannot continue to neglect those few Muslims, and others, attempting to take on this threat within their own communities.

For now, my guess will be that these attacks will only aid the anti-immigrant rhetoric of France’s far right, sweeping xenophobes to prominence, further polarizing communities, which for good or for bad, will only sustain the process of radicalization even further. This is so despite the fact that France has taken hardly any Syrian refugees, and Germany, which has taken hundreds of thousands, has yet to be hit as hard as France has. European born and raised jihadists have so far posed the biggest problem, not immigrants.

What is clear to me is that if indeed this turns out to be an official ISIS attack, it would be the most sophisticated one in Europe yet. In such a scenario, all our calculations about what is required at home, what must be done in Syria to tackle ISIS head on—and how to truly defeat the appeal of the Islamist ideology—must be fundamentally reappraised.

GALLERY: Photos From the Attack on Paris (PHOTOS)