The airport is also shared by a German City although they don't have a direct road to the airport ( except going via France or Switzerland.
I think it is Freiburg but I'm not sure. The name of the city is also on the busses that bring you to the plane.
The France-Swiss border as well as the France - Germany and Germany - Swiss borders are only a few km away.
Like already posted by TR, the airport is located in France but there is a direct road from Basel ( Switzerland ) to the airport.
If you arrive you can choose that you enter France or Switzerland ( two different customs ) and there are two seperate check-in halls.
That was the situation 2-3 years ago, but then there was a maquette of a new building. I don't know that it is already build and how it works there. I would think it is the same as back then.
Basel is also the base of Cross Air