From my reading of the relevant wikipedia page is looks like ESA gets the private company EAD Astrium to develop Ariane launchers and Arianespace, which is also a private company, to actually launch them and market them for commercial launches:
Arguements about government ownership of EADS aside - the important part is that ESA is free to launch on Ariane, Soyuz, Chinese or any other rocket without it becoming a congressional matter.
http://en.wikipedia.org/wiki/Ariane_%28rocket_family%29