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. Only Borini Bus run a direct service from from Geneva airport to St. Gervais priced at 42 euros. La Fayet, a few kilometers away is also served by coaches with a single journey costing around 30 euros, and then a 10 euro taxi. Unfortunately taking public transport from Geneva airport to St. Gervais involves a gauntlet of trains, trams and buses and at least 2 hours hence why the pricey coach services exist. Don't be worried by website requests to book your coach ticket in advance, you can easily get bus tickets in the arrivals hall.