Tousignant studied with Luis de Pablo at the University of Ottawa, where he earned a B MUS in composition in 1977. He then studied under Max Deutsch at the École normale de musique in Paris (on a Canada Council grant) and received his Licence composition there in 1979. In 1985, he earned a D MUS in composition at the Université de Montréal, where he studied with Serge Garant.
In 1982, Tousignant’s work Durée won the second prize of the Sir Ernest MacMillan Award/Fellowship awarded by CAPAC. In 1984, he wrote the music for the mass celebrated in Ottawa during the visit of Pope John Paul II. In 1984–85, he was music director of the contemporary music concert series presented at the Maison du Citoyen in Hull, Quebec.
A grant from the University of Ottawa allowed Tousignant to study at the Institut de Recherche et Coordination Acoustique/Musique (IRCAM) in Paris (1986–87). Following a teaching appointment at the University of Ottawa (1986–88), he became a professor at the Université de Montréal in 1988. In 1987, he sat on the jury of the Canadian section of the International Society for Contemporary Music (ISCM). In 1988, he took charge of the introductory lectures to contemporary music concerts at the National Arts Centre in Ottawa.