There are a number of reasons. A lot of people, francophone or anglophone, come to the Yukon because they are attracted to the wide open spaces. They may also be attracted by employment possibilities in the Yukon, especially in mining, an industry that is picking up again.
As for francophones, some people have immigrated to the Yukon from Europe. Previously, the Association franco-yukonnaise participated in Destination Canada, a job fair held in France and other French-speaking countries to recruit immigrants. The AFY was able to participate because, at the time, it received joint territorial-federal funding. But that funding was eliminated. The fair let us recruit people who were really interested in leaving an overcrowded homeland and settling in the Yukon.
Before leaving, or even when they arrive, they do research on the lifestyle that the Yukon can offer. Families appreciate having access to French-speaking daycare and to other services in French. Francophones, especially those with families, settle in the Yukon because they can live a good part of their lives in French there.