By plane:
To Geneva airport with direct access to the train going  to Martigny (20 minutes drive from chalet), or even with the mountain train  "Saint Bernard Express" direct to Etiez ( 5 minutes drive from chalet)
Swiss, Air France and EasyJet fly to  Geneva.
Compare and then, buy!
http://www.easyvols.fr/index.jsp?clientId=2&xtor=SEC-12
http://www.kayak.fr/flights?ispredir=true
http://www.liligo.fr

By train:
Paris - direct or change at Martigny Lausanne and Martigny
http://www.sbb.ch/fr/
http://www.voyages-sncf.com/billet-train?&prex=T_KWG_goo&mcp

By road: 
http://www.viamichelin.fr
- Either through Geneva and along Lake Geneva, Lausanne, Montreux to Martigny, then to Grand Saint Bernard - Verbier - Vollèges - Route du Levron - Cries.
- Either through the Jura and the border at Vallorbe,  Lausanne, to reach Martigny, then to Grand Saint Bernard - Verbier - Vollèges - Route du Levron - Cries.

But the real good thing is to come by car!