He has won ten Vanier Cups as head coach with the team, the most by a single head coach in U Sports football history.
He was named coach of the year in 2005 and in 2010.
As head coach, Constantin has an all-time record of 178-30 (127–20 in regular season; 51–10 in playoffs), with 14 Quebec championships as of 2018.In 2010, the Rouge et Or won the Vanier Cup against the Calgary Dinos, 29–2, after thirteen straight victories, which was a first in CIS football history.
In 2014, his football team established a new CIS record with 22 straight wins.