It’s no surprise that Britain’s decision to extend its military efforts against Islamic State with airstrikes in Syria has been met with a sigh of relief in France. It was appreciated both as a vindication of François Hollande’s strategy of reaching out to allies after the Paris attacks, and as a welcome break from what had been perceived in recent years as a worrying British strategic withdrawal from European security issues.

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From a French perspective, that was starkly illustrated by Britain’s refusal to join airstrikes in Syria in 2013, at a time when the chances of getting President Assad to the negotiating table were possibly at their highest. However, where to go from here is now the key question.

There is no escaping the fact that the UK and France are two medium-sized powers with constrained resources. On their own, the influence they can bring to bear on the Middle East has its limits. As the US vice-president, Joe Biden, said recently to reporters: “We [the US] have been doing it all, basically.” How the two European nations manage to frame the campaign against Isis – a danger that is international and domestic – will go a long way to defining whether the continent can pull out of its doldrums and build itself up as a global force.

The backdrop to this is that America’s commitment to European security has altered as it focuses on other, mostly Asian, issues. Asking how Britain’s decision to strike in Syria can affect the overall picture in fact raises the question of what Europe’s impact can be. Breaking out of nationally focused debates on strategy, however passionate, appears urgent. Europe’s crises are all interconnected: the violence and radicalisation spewing out of the Middle East, the rise of populist movements, the difficulties in addressing the refugee crisis, and the growing assertiveness of Russia. For a while now, Germany has come across as the natural leader on many issues. But European security is an area where France and Britain could have greater influence.

Building up European momentum on the Middle East, relative to the US, is of course a tall order. One step forward was taken this week, when the Bundestag authorised German participation in the air campaign in Syria, through refuelling and reconnaissance flights. Although this doesn’t include airstrikes, it is the first time since the second world war that Germany has committed to offensive military operations outside Europe and outside a Nato framework.

When French MPs discussed Syria, it was clear they weren’t inhibited by past toxic mistakes

Involving more European countries in the anti-Isis strategy makes sense, if only to avoid reigniting the legacy of the colonial era and all the suspicions still attached to it. Memories of Franco-British alliances in the Middle East include episodes such as the 1916 Sykes-Picot agreement, which carved up the Ottoman empire, and the disastrous 1956 Suez expedition.

But if there is one huge difference between the way the French and the British approach Middle Eastern affairs, it comes from the fallout over the 2003 Iraq invasion – a conflict mentioned several times during the House of Commons debate this week. France vigorously opposed that war.

When the French MPs discussed Syria one week earlier (with an overwhelming majority of 515 votes for prolonging airstrikes, and only four against), it was clear they weren’t inhibited by past toxic mistakes. The ruling Socialist party has shown no qualms about military action – as opposed to Britain’s tortured Labour party, still traumatised by Tony Blair’s alignment with George Bush.

The wider European picture also means that fighting radicalisation and “foreign fighter” networks should not entail just police and intelligence cooperation, but also shared experiences on how to create better inclusiveness for Muslim populations.

After the 7/7 bombings in London, many French commentators waxed heavily about the limits of British multiculturalism and London’s “excessive tolerance” of radical Islamist groups in the 90s. After the Charlie Hebdo tragedy, and now Paris, just as many comments were made in Britain about France’s brand of secularism and its disenfranchised second- or third- generation immigrant youth. Surely it might help for French and British civil society organisations to come together, rather than attack each other’s models?

Getting the balance right between fighting the external dimension of Isis (its self-proclaimed caliphate in Syria-Iraq) and countering its internal dimension in Europe (its terror cells and ideology) will be essential. That can happen only if Europe together thinks more strategically about its security and domestic challenges.

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The European Union can, if it acts together, put pressure on Turkey, Iran and others to address the complex diplomatic issue of finding a settlement in Syria. Together, also, it should reflect on how to balance domestic security with fundamental values (instead of individual nations rushing to adopt ever more repressive legislation).

The Paris attacks were a watershed: Europe’s stability and safety have been dramatically challenged. To its east, Russia and Ukraine; and to its south, the Middle East, and jihadi groups in North Africa, where Libya is key.

The British vote for airstrikes shouldn’t be seen as just a gesture towards an old ally, after France called for help – however important that was. It should be the start of a collective security awakening for Europe.

Describing Isis as a new fascism that democracies must crush is a strong, compelling argument. But because the Middle East is so close and connected to us, that fight needs to be seen as European – not just B ritish and French.