PARIS—The eurozone economy kept pace with that of the U.S. for the first time since 2008 last year and its jobless rate fell to a seven-year low, putting the currency area on a steadier footing at the start of a year clouded by political uncertainty.

A fourth-quarter pickup allowed the eurozone economy to expand by 1.7% compared with 1.6% for the U.S. in calendar 2016, demonstrating the currency zone’s resilience in the face of repeated shocks to confidence, including the U.K.’s June vote to depart the European Union and terrorist...