In Denmark we have switched largely to solar and wind with backup provided by burning of biomass (largely imported wood pellets from Canada and the USA, but also domestic bio-trash which is sorted separately in many homes).
But even without that, nuclear, wind and solar combined with lots of batteries (stationary and in all the cars) seems like a totally achievable solution. Especially in Europe and America where you have lots of varied geography and can get hydro, solar, thermal and wind to supplement each other, see example the plans for Denmark (wind), Norway (hydro), UK (nuclear).
Even in this already a few year old data you linked, the fossil fuel share has gone from 70%+ to just 30% since 2005. That's nothing short of amazing, and the trend is clear.
But even without that, nuclear, wind and solar combined with lots of batteries (stationary and in all the cars) seems like a totally achievable solution. Especially in Europe and America where you have lots of varied geography and can get hydro, solar, thermal and wind to supplement each other, see example the plans for Denmark (wind), Norway (hydro), UK (nuclear).