I don't think they'll achieve an outright ban, but we probably will see a limit on capacity for ICE engines, and see them disallowed in trucks and other heavy vehicles - they account for a majority of emissions.
Market demand will take care of the rest, as I don't think there'll be much interest in new fossil cars once electric is cheaper and more powerful, which is happening as we speak.
Also, VW probably achieved a stonking own goal with the emissions scandal - many who bought "eco" cars thinking they were doing their bit have been let down, and the Germans are an environmentally conscious lot.
Me, I've been putting my money where my mouth is and buying nice houses on busy noisy roads. They'll still be busy in ten years, but quiet and no longer polluted - and once driverless tech is firmly in, congestion and density go away too.