I think it will mean some sort of change in driving habits. It costs me about €80 to fill the tank at around €1.55 or so per litre at the moment. Stick that up to €2 a litre and it's going to cost well over €100. It amounts to the same thing but I think that notional amount will mean more to people than it being €2/l.
Whether it moves people to bikes, that remains to be seen.
Does anybody know, offhand, the average distance that people live from work?
Personally, I drive 60km to and from work (120 total per day).
As ever, 'average' is limited in what it tells us. Mode and median too would be more enlightening but there you go.