The pro-independence Caledonian Union will drop one of its ministers when the collegial government is renewed in the coming weeks.
The party has announced that Anthony Lecren won't represent it when Congress is convened to appoint a new executive.
Last year, he was given a suspended six-month jail sentence for assaulting his former partner and a suspended two-month sentence for drink driving.
Anthony Lecren has been a minister since 2011.
A change of government is due because the budget minister Philippe Dunoyer is expected to resign in order to keep his seat as New Caledonia's member of the French National Assembly.
Under the provisions of the Noumea Accord a single resignation triggers the fall of the government and the entire executive needs to be renewed.
The Accord also provides for parties in Congress to have the same proportion of seats in the government.