EuroVelo 6
The EV6 traverses ten countries, from the mouth of the Loire eastward along that river to the Saône, across the border to Switzerland, along the Rhine to Lake Constance, north into Germany, down the Danube and through Austria, Slovakia, Hungary, Serbia, Croatia, Bulgaria, and Romania to the Danube Delta, before terminating at Constanța on the Black Sea.
Apparently this is the best one for a first timer? I might have a new fixation.