The visit of the French president was happily timed to draw headlines at home away from the regional election results. It seemed to go well. Sarkozy spoke to a packed attentive house at Columbia University. He performed deftly at his White House press conference (putting Obama on the spot over EADS by saying, "He is a man of his word"). And with his elegant wife he was treated to a rarely bestowed supper a quatre with the US president and First Lady.
Speaking about Obama at home, his tone had been more critical of late. Like other European leaders, he evidently feels that the administration is neglecting them, preferring to develop new partnerships elsewhere, notably with China and Russia. (With mixed results. Outreach to Russia has borne fruit on nuclear arms reduction. The effort to get on with China seems to have stalled.) Feelings in Britain are especially bruised. You could argue that Gordon Brown has been snubbed, not merely neglected, by Obama, notwithstanding Britain's large and politically taxing commitment in Afghanistan.
This recent piece by Robert Kagan was on to something. You seem to get more warmth from Obama as an adversary than as a friend.
This administration pays lip-service to "multilateralism," but it is a multilateralism of accommodating autocratic rivals, not of solidifying relations with longtime democratic allies. Rather than strengthening the democratic foundation of the new "international architecture" -- the G-20 world -- the administration's posture is increasingly one of neutrality, at best, between allies and adversaries, and between democrats and autocrats.
Sarkozy prepared for this trip by criticizing US policy and advertising the limits to French cooperation with the US. He was warmly received as a result. If I were advising Brown on managing his own relationship with Obama, I'd say, "Forget the special relationship--it means nothing to Obama. No more reflexive support of the US. Follow Sarkozy's example, and things will warm up directly."