PARIS — Europe is so besieged by problems that on some days it looks as if its common currency and hopes for unity are disintegrating. All the same, Nicolas Sarkozy will head to Washington early in January for a conversation about reorganizing the world monetary system in a way that might just mark the United States as the real global force in decline.

For the last two years, the French president has been arguing that the dollar’s role as the single global reserve currency doesn’t reflect what he insists is a multipolar world with no further reason to kowtow to the greenback.

Now, as president and agenda setter in 2011 of the Group of 20 consultative body of leading economic nations, Mr. Sarkozy is leaving his bully pulpit’s specific aims and tactics on the dollar fluid — an imprecision difficult to avoid against a background of the euro’s daily ducks and dives.

Still, in the words of Le Monde last month, he is “counting on making the G-20 his magnum opus and finding a solution to the world’s monetary imbalances with, if necessary, a common French-Chinese front against the United States.”