France’s annual rate of inflation has risen in May at a faster pace than in April, beating forecasts and posting the highest reading since September 1985, according to preliminary data released by French statistics office Insee on Tuesday.

Consumer prices rose 5.2% on year measured by national standards, against the 5.1% forecast by economists in a Wall Street Journal poll. They rose 4.8% on year in April.

By European Union-harmonized standards, consumer prices rose 5.8% on year in May, following a 5.4% rise in April.

Consumer prices rose 0.6% on month in May, in line with the forecasts of economists polled by The Wall Street Journal. This followed a 0.4% rise in April.

Write to Maria Martinez at maria.martinez@wsj.com