More, earlier French help to Saddam
Early, but small POD with no effect on fall of Communism : France decides to take a stronger anti-Israel and pro-Iraq stand after Israel bombs the reactor in 1981. No significant change to OTL in Europe but France begins to supply Iraq with better weaponry and technical support, interfering more in Iran-Iraq war and getting enhanced access to Iraqi oil. France also begins to more vigorously condemn Israel, esp. the Lebanon incursion/occupation, including campaigning for an EU embargo. Both enhance France's visibility in the world and Paris gains significant support in the EU (from the Benelux and Nordic countries, say). The US winks at the first move for a time but not the second. Iraq still demands compensation from other Arab states for fighting off the Aryan invader and attacks Kuwait sometime after war ends with Iran. Only now it has had essentially a decade of very close ties with France . . .
Alternately, push the 1990 Iraq invasion of Kuwait back a few years, allowing France to jump in post fall of Communism in Europe. The France-Iraq tie isn't as strong but the US-led expeditionary force suffers more losses than in OTL due to French aid to Iraq and discovers a good deal of French weaponry. Franco-American relations head south, with more and more of Europe forced over time to choose one side or the other on a variety of issues. Starting around 1997, stronger anti-Jewish bigotry in France for any of several reasons lead to open attacks on Jews by French and resident immigrant Muslims, which the authorities ignore. By the time of the hotly contested 2000 US Presidential campaign, candidates are falling all over each other demanding action against French "racism." American (self-)righteous indignation does not sit well with much of the EU, especially those with growing Muslim populations of their own. In 2001, Muslim terrorists launch a deadly attack on American civilians. Not only does a block of the EU refuse to cooperate with any American military retaliation, it turns out some of the Muslims had been living in France . . .
Picking on France in a way but I can't see any other EU country taking the lead on anything which might produce a military conflict with the US. Following yes, leading no.