The French AutoRoute Blanche (A40) ends a few kilometers from St. Gervais where it begins the climb up to the foot of Mt. Blanc and the tunnel that leads to Italy.
The nearest major airport is in Geneva (GVA)  about 45 minutes away by car and is serviced by most major European airlines.
St-Gevais-Le-Fayet, a few kilometers away from the skiing, is served by coaches with a single journey costing 19 euros with Ouibus  at the time of writing; the bus stops outside the rail station. Either a taxi or another Ouibus (often timed to leave literally fifteen minutes after the first arrives) for an extra 6 euros; that Ouibus will drop you at the end of the "Viaduc de St Gevais". Ouibus will get you all the way there in eighty minutes; you can buy the ticket all the way to the Viaduc as a single ticket. In theory, if you've bought the ticket all the way, the connection knows you're coming and might wait on a late connection.