LaFrance was born in Chapleau, Ontario, just outside of Sudbury. He would play with several junior and senior teams in the Sudbury area. He was a key member of the Sudbury Wolves team that won the Memorial Cup as Canada's national junior champions in 1932. LaFrance scored the overtime game winning goal in game two of the series versus the Winnipeg Monarchs.
The 5'10" 165lb left winger was given a five game look by the Montreal Canadiens in the 1933-34 season. The team paid his train fare and brought him on board late in the season. He would play three games in the regular season and another two in the Stanley Cup playoffs. Aside from a minor penalty, Adie LaFrance never got on the score sheet.
LaFrance was brought in as an injury replacement for Georges Mantha, who broke his foot. LaFrance slotted in on a line with Jack Riley and Paul Raymond. He debuted against the Ottawa Senators.
Inspired by his tryout LaFrance turned pro in 1934-35. He would play a season in Quebec City and four seasons in Springfield before retiring. He would never get back to the National Hockey League, with the exception of an exhibition match against a local team in Saint John, New Brunswick in October, 1934.