I submit the situation would have been French (not American) banks defaulting on their US Dollar obligations, which is a problem for the Banque de France and by Extension the ECB which had to be rescued by the Fed.

You'll remember Dean Baker's Time for the Fed to Take Over the European Central Bank's Job

In this case the Fed would be intervening in the European economy for the same reason as China - to sustain our domestic economy. If the eurozone collapses, there are no easy tools in the Fed's bag of tricks that will allow it to quickly offset the negative impact on the U.S. economy. It would make far more sense to act preemptively to prevent this disaster from happening. This can be seen as an essential part of its legal mandate to maintain full employment.

Of course this sort of intervention will look horrible from the standpoint of the eurozone countries. It will appear as though they cannot be trusted to manage their own central bank and deal with their own economic affairs.

Unfortunately, this is the case. They have entrusted the continent's most important economic institution to a group of ideological zealots who are infatuated by the sight of low inflation rates even as whole economies collapse in ruins and tens of millions of people needlessly go unemployed.

Perhaps the Europeans will respond to this affront by putting some serious people in charge of the ECB who are committed to maintaining a functioning economy in the eurozone.  If that is the outcome, it will be a win-win for all involved. But if they can't rise to the task, we should not allow the ECB ideologues to wreak havoc on the lives of tens of millions of innocent people in Europe, the developing world and here in the United States.

There are three stories about the euro crisis: the Republican story, the German story, and the truth. -- Paul Krugman