IT IS NO EASY JOB, being the grand negotiator at almost every financial crisis in the world in these troubled times. But as head of the International Monetary Fund, or IMF, Christine Lagarde has played a role in dealing with everything from the Cyprus bank scare to Chinese exchange rates.

A lawyer by training, she came to the post after a six-year stint in the French cabinet. She is described as warm, informal—and highly disciplined. She was, after all, a member of the French national synchronized swim team in her youth,...