Currently, under the Official Languages Act, airport passenger services must be offered in both English and French. This obligation applies to airport authorities, but the airport authorities impose the obligation on air carriers.
In the example you gave, if someone arrives at the counter in Vancouver, they have the right to be served in French. As for a Vancouver-Calgary flight, there would be no service in French because the cities are not designated areas. However, for the second leg of the flight, from Calgary to Ottawa, inflight service would be available in French, because Ottawa is in a designated area. Departing from Vancouver, service at the airport would be in French. At the Calgary airport, service would be in French. Upon arrival in Ottawa, service would be in French. In flight, service would be available in French between Calgary and Ottawa.