PARIS, April 30 (Reuters) - French and eurozone inflation data released on Tuesday boosts confidence the European Central Bank will be able to start lowering interest rates in early June, ECB policymaker Francois Villeroy de Galhau said.

French and broader eurozone inflation held steady in April at 2.4%, with underlying prices pressures in the shared currency bloc easing slightly, official data showed earlier on Tuesday.

Villeroy, who is also governor of the French central bank, said that the data boosted confidence that inflation would return to the ECB's 2% target by next year.

"We should therefore be able to start cutting rates in the beginning of June," Villeroy said on social network Linkedin.

"The speed of cuts should afterwards be set pragmatically depending on the inflation outlook beyond the month-to-month results, which could show a certain volatility," he added. (Reporting by Dominique Vidalon and Leigh Thomas; Editing by Benoit Van Overstraeten and Alex Richardson)