Investors expect her to follow her predecessor, Mario Draghi, and do “whatever it takes” to defend the euro. But Ms. Lagarde, currently the managing director of the International Monetary Fund, is not an economist, and that has raised questions about her candidacy.

Her qualifications: Ms. Lagarde trained as a lawyer before becoming a minister in the French government. Supporters point out that the I.M.F., which she has led for eight years, played a crucial role in preventing the collapse of Greece ’s banking system during the eurozone debt crisis.

Management style: Ms. Lagarde once said she tried to do something for women every day. She can be expected to address a gender imbalance at the central bank; just two of the 25 members of its governing council are women.

What’s next: European finance ministers easily endorsed Ms. Lagarde last week. The European Parliament and the central bank’s governing council will now weigh in, though neither has the power to block her from taking charge on Nov. 1.