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Drafted to the NHL by the Islanders 65th overall in the 1972 NHL Amateur Draft following a good junior career with the Rosemont National, the Quebec Remparts and the Verdun Maple Leafs, Grenier enjoyed his first NHL action in 1972-73. He played in 10 games, scoring once and adding one assist. Unfortunately for him, if NHL action came early in his pro career, it just never happened again. He played in the American Hockey League, the Central Hockey League and the North American Hockey League before major league became a reality again, as he joined the Quebec Nordiques. He split the season between the World Hockey Association's Nordiques and their NAHL farm team, the Maine Nordiques and didn't do bad in the WHA, with 11 goals and 9 assists in 34 games. That was not sufficient however to secure a permanent spot with the team and Grenier was back in the AHL the next season.
In 1980, Grenier flew over the Atlantic to try his hand in Europe. He had a very succesful season in Finland with Reipas Lahti in 1980-81; the next season, he also enjoyed a good campaign with EHC Arosa of the National League A in Switzerland. He also played in Austria for Villach SV, the Vienna Capitals and VEU Feldkirch. He acted as a player-coach in Villach in 1985-86, finishing the season with a 16-10-4 record.