STRASBOURG, France—Pope Francis called for Europe to find a new sense of purpose, describing the Continent as “elderly and haggard” as it struggles with high youth unemployment, waves of migrants from strife-torn countries in Africa and the Middle East and conflict on its eastern borders.

The pope made the remarks Tuesday in an address to the European Parliament, the first pontifical visit to the body since a 1988 trip by St. John Paul II. In his address, Pope Francis—the first non-European pope in centuries—touched on the...