Underlying the shift is a fear of the deteriorating security situation just across the water from Europe and, in particular, of Islamic fundamentalism. The EU plans a summit in Barcelona in November to address the issue.
There are obstacles: one is that different countries see different things when they look at the Arab world. Britain and the other northern European states see mainly the eastern Mediterranean, the Middle East peace process and oil. Europe's southern states see the Maghreb, Islamic fundamentalism, the threat of conflict and refugee flows. France has fought a long battle to get British and German intelligence to prioritise Algeria - a battle that it is now winning. The US, for its part, still sees things through the prism of Israel and the Gulf.
The problems of the south did not loom large on the EU agenda when Denmark, Britain, Belgium and Germany held the EU presidency, and though Greece tried to put the subject under the spotlight, it lacked the political clout. The presidency is now held by France, to be followed by Spain and Italy. No wonder things are changing.
The sticking point may be cash. Spain's Manuel Marin, the ambitious EU commissioner for Mediterranean affairs, wants 5.5bn ecus for North Africa and the Middle East as part of a radical new policy thrust. But the funds of the EU are far from inexhaustible, and the main net contributors to the budget are Germany, Britain, France and the Netherlands; only Paris is truly agitated about the situation in the Mediterranean.
The EU is already negotiating "Euro-Med" agreements with Morocco, Tunisia, Israel and Egypt, and hopes to start soon with Jordan. It also has economic and political accords with Israel and Syria.
The Commission hopes that the new approach will go further than this rather fragmented, bilateral approach and treat the Mediterranean region as a whole. The problem is that there is little agreement on what the region is, let alone what its problems areand how to solve them.