Meyers, 34, was the star of TV's "The Tudors." His film credits include "Michael Collins," "Velvet Goldmine," "August Rush," "Vanity Fair" and "Match Point."
UsMagazine.com said the Golden Globe Award-winning actor was ordered to pay the fine and given a one-month suspended jail sentence Wednesday.
He had been charged with drunk and disorderly conduct for allegedly striking a bartender in June 2009 at Charles de Gaulle airport, then threatening to kill the police who responded to the scene.
Meyers later apologized for his behavior, explaining he has long battled alcoholism. He has since gone to rehab several times.
2014: The Year in Music [PHOTOS]