The country where the Danube River does not flow or touch is France. The Danube River receives it water from nineteen countries, but it only flows or touches ten countries and France is not one of them. The countries which the Danube flows through or touches are as follows: Austria, Hungary, Slovakia, Serbia, Croatia, Romania, Bulgaria, Ukraine, the Republic of Moldova and Germany where the river originates.
The primary source of the Danube River is Breg which is located in Martinskapelle, Black Forest Germany and its second source is Brigach which is located in St. Georgen, Black Forest, Germany. If you are to combine the total length of the Danube River, you would get 2,860 kilometers or 1,777 miles in length.