He served as bishop of the Roman Catholic Diocese of Jacmel from 1988 to 2009.
He then served as bishop of the Roman Catholic Diocese of Les Cayes from 2009 to 2011.
Poulard served as archbishop of the Roman Catholic Archdiocese of Port-au-Prince from 2011 to 2017, succeeding Joseph Serge Miot, who died due to the 2010 Haiti earthquake.
[1] His resignation was accepted by Pope Francis on 7 October 2017 due to reaching the age limit, while appointing Max Leroy Mésidor, until then Archbishop of Cap-Haïtien, as Archbishop of Port-au-Prince.
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