Finnie grew up in Ottawa, and played for the Ottawa Aberdeens. In 1904–05, after the retirement of Bouse Hutton, he became the starting goalie for Ottawa. The team was the reigning Stanley Cup champion by winning the FAHL season and a Stanley Cup challenge by Dawson City. He was the Ottawa goalie only for the one season. Billy Hague would win the job the next season. He played for the Montreal AAA in 1907–08.