A French colonel, Francois-Xavier Yves, stood on the roof of his mechanised infantry battalion's barracks to explain his colour-coded ethnic charts to us. Red for Serbs, blue for Albanians, green for Bosnians, orange for Turks. Across the Ibar river, northern Mitrovica was a crazy quilt, predominantly red but intermingled with other colours.
In three ethnically mixed high-rise towers to the left of the bridge, 560 residents must present a badge to French soldiers every time they enter their building. The chart shows the ethnic group of every apartment on every floor. It's a long way from liberty, equality and fraternity, Col Yves admits, "but it's the way they want it. If you say `hello' in the wrong language, they won't answer."
Col Yves believes that he is helping to build what the French call "L'Europe de la defense" by preventing the hateful neighbours of Mitrovica from killing one another. "If we don't create a European defence system we'll always be the Americans' lackeys," he says with a frankness you don't find at Kfor headquarters in Pristina. "The Americans see and hear everything; we're always dragging behind them."
The colonel argues that "Kosovo is a European affair - it's only two hours from Paris." Perhaps, but 75 per cent of the munitions used in the 1999 NATO bombardment were American. So were most of the communications. And the US maintains the largest contingent.
The agreement which ended the bombardment foresaw an "international force" in Kosovo. Former president Milosevic claimed it would be a UN, not a NATO force. But the blue and white badges worn by Kfor personnel say NATO. The NATO symbol is everywhere, and the flags of 19 NATO countries line the main hall at headquarters in Pristina.
"There's not even a Partnership for Peace flag," an Irish officer says wistfully. Despite the formal UN mandate for the force Europe's four neutral countries are second-class citizens in Kfor, with a lower security clearance than non-EU Poland, Hungary and the Czech Republic, who joined NATO last year.
During its EU presidency, France is actively promoting the establishment of a European rapid reaction force - agreed in Helsinki last December - and European defence in general. Officers from the five-nation (France, Germany, Belgium, Spain and Luxembourg) Euro corps in Strasbourg are about to complete a six-month tour at Kfor command, where they filled 350 of 900 positions. The US initially resisted Eurocorp's offer.
The French general, Jean-Philippe Wirth, called the experience the Eurocorps' "baptism of fire" - perhaps an overstatement for a grouping created seven years ago. Aside from the French, most of Kfor's contingents seemed unaware that the Europeans had played any particular role for the past six months. "European defence?" a Danish officer said. "As far as I'm concerned, this is a NATO operation. Full stop."
After France, Germany is the most enthusiastic forger of a "European defence identity", not because Berlin believes US "hyper power" is dangerous, but because a common defence policy is deemed necessary for successful political and economic integration.
On the ground in Kosovo, obstacles range from Italian drivers who cannot understand requests made by French officers in English, to mutual back-biting by the French and British.
We were given an introduction to Kfor by a young British major who turned to a US colonel at the back of the room each time a journalist asked a difficult question.
NATO's Secretary General, Lord Robertson, admitted last March that the US air force fired 31,000 rounds of depleted uranium (DU) - a waste product of the nuclear industry used for its armour-piercing abilities - during the 1999 bombardment. Some scientists believe DU may be the primary cause of a sharp rise in cancer cases in Iraq and the "Gulf War syndrome" which afflicts soldiers who fought there.
Several high-ranking Kfor officers dismissed questions about DU in Kosovo, claiming it was not dangerous, that they did not know where DU rounds were fired and that no precautions have been taken. The US colonel at the back of the room insisted a recent course on radiation in the Ukraine for members of the Kosovo Protection Corps - the recycled Kosovo Liberation Army - had nothing to do with DU. Yet Dr Bernard Kouchner, the head of UNMIK, acknowledged that Kfor received the results of a DU study within the past week. Use of the munitions represented "not a short term but a long-term risk", he said.