Léveillé won a seat to the Legislative Assembly of Quebec in 1966 in the district of Maisonneuve and was a member of the Union Nationale.
Léveillé lost his re-election in 1970 and was succeeded by Parti Québécois (PQ) candidate Robert Burns.
Out of politics, Léveillé worked as a realtor and served as a commissioner of oaths, accepted several other public appointments, and operated a small publishing company in the 1970s and 1980s.
Léveillé finished a distant fourth in his own district against Louise Harel with 1.3% of the vote.
[4] The Union Nationale would not contest another general election prior to being deregistered by the Chief Electoral Officer of Quebec in 1989.