When Mehdi Nemmouche, a French jihadi, made his way home from the Syrian battlefield in March, he crossed borders with the same ease as millions of other European travellers.

He went first to Istanbul, then Malaysia, Singapore and Hong Kong before flying to Frankfurt and then continuing to his native France. Weeks later, it is alleged, Mr Nemmouche crossed another border to brutally murder four visitors to the Jewish Museum of Belgium in Brussels.

As fears mount of other European jihadis returning from Syria to launch terrorist attacks on home soil, Mr Nemmouche’s travels are weighing heavily on the continent’s security chiefs, who find themselves grappling with one of the EU’s most cherished multilateral projects: the Schengen agreement that facilitates border-free travel.