Kirsch, who joined the Department of External Affairs of Canada in 1972, has held a number of positions in the Department, including Assistant Deputy Minister for Legal, Consular and Passport Affairs, Ottawa (1994–1996); and Director General, Bureau of Legal Affairs, Ottawa (1992–1994).

Kirsch is member of the Bar of the Province of Quebec and of the Canadian Council on International Law and was appointed Queen's Counsel in 1988.

Kirsch served as Chairman of the Drafting Committee of the International Conference on the Problem of War Victims (1993), Chairman of the preparatory and subsequent Intergovernmental Working Groups of Government Experts on the Protection of War Victims (1993, 1995), and Chairman of the Drafting Committee at the 26th and 27th International Conferences of the Red Cross and the Red Crescent (1995, 1999).

He has extensive experience in the development of international criminal law with regard to issues such as various acts of terrorism; suppression of unlawful acts against the safety of maritime navigation; unlawful acts of violence at airports serving international civil aviation; safety and security of UN and associated personnel and the taking of hostages.

In 1998 Kirsch served as Chairman of the Committee of the Whole of the Diplomatic Conference of Plenipotentiaries on the Establishment of an International Criminal Court.