The Haute Savoie is close to the border with Switzerland and has short, easy transfers from Geneva International Airport (around one hour). The area is also within reasonable distance of Lyon and its international airport, Chambéry airport in Savoie and Grenoble airport in Isère. There are shuttles from the major airports. Some family ski holiday packages include flights and sometimes also transfers.
For getting to the French Alps by train, see the excellent Man in Seat 61 (seat61.com). Cluses (30km, with TGVs from Paris) and then Geneva (70km) are the closest train stations to Flaine.