Father Morice was born and raised in France, in the commune of Saint-Mars-sur-Colmont in the département of Mayenne. As a seminarian he was inspired by Father Émile Petitot and set himself the goal of becoming a missionary and explorer in Northwestern Canada. He arrived in British Columbia in 1880, and after a stint in Williams Lake at St. Joseph's school, where he studied Chilcotin and, with the aid of Jimmy Alexander, the son of a Carrier woman and a fur trader who was sent to St. Joseph's School, began his study of Carrier.
In 1885 his dreams were realized and he was posted to Fort St. James, the fur trading and missionary center in the Carrier region. Father Morice rapidly learned the Carrier language and became the only missionary to speak more than rudimentary Carrier. Within a few months of his arrival he created the first writing system for Carrier, the Carrier syllabary, by making a radical adaptation of the Cree syllabics. From 1891-1894 he published a bimonthly newspaper, the Dustl'us Nawhulnuk, in Carrier. He was responsible for the translation of the catechism and many hymns and prayers into the language. From this, Father Morice was the first person to recognize all of the phonological distinctions in an Athabascan language and write it accurately. He was also the first person to make extensive transcriptions of material in an Athabascan language. His magnum opus was his massive two volume The Carrier Language: A Grammar and Dictionary, which immediately made Carrier by far the best documented Athabascan language of the time.
Father Morice would have preferred to remain in Fort Saint James but in 1904 he was withdrawn by the bishop, who finally paid heed to the complaints of the Hudson's Bayfactor. Father Morice proved unwilling to perform the other duties the bishop assigned him and unable to get along with other priests, so after several years of conflict the Church set him up in a house in Winnipeg where he spent the remainder of his life as a scholar, writing extensively on Carrier language and culture, more general Athabaskan topics, the history of the Roman Catholic church in Western Canada, the history of the French and Métis of the West, and occasional other topics.