France is in a quiet sulk. Nicolas Sarkozy is the most pro-American president of the Fifth Republic. He brought France back into NATO’s military command, rejected the de rigueur cynicism of French political discourse on the United States, and reached out to Obama. For all of which he got nothing. He must hear de Gaulle’s ghost at night whispering, “I told you so.”

In London, the British are shaking their heads. Prime Minister David Cameron, knowing Obama’s cool, set expectations low but is looking for a way to re-energize a special relationship shaken by the Iraq war. He has found little responsiveness in Washington. Elizabeth Sherwood-Randall, the senior director for European affairs at the N.S.C., is widely viewed as dismissive of British concerns.

“The special relationship is in real trouble,” said Julian Lindley-French, a defense expert at the Dutch Royal Military Academy.