It’s just under a 10-hour drive from the Channel port/Eurotunnel hub of Calais to the départementale capital Gap.  

Fast TGV trains from Paris to Gap take just over five hours, or you can take a TGV to Oulx in Italy (4 hours 30 minutes), which is 30 minutes from Montgenèvre. 

Turin airport in Italy, served by low-cost flights, is an hour from Montgenèvre. Or you could fly into Marseille, from where the Train des Neiges runs to the Hautes Alpes resorts every Saturday and Sunday in the season. The train also picks up in Aix en Provence, so you could take the TGV to there. Or there are Navettes Blanches (‘white shuttles’) from Marseille and Aix every Saturday from December to April.
Grenoble and Lyon airports are further possibilities.