In Germany, like the AA in the UK, they operate their own recovery and roadside assistance vehicles. Elsewhere they subcontract to partner organisations such as the AA in the UK.
In addition they have offices in many countries. I called their French office and my conversations were direct with ADAC. Both people I spoke to spoke excellent English so there were no language issues.
I am just making people aware that roadside recovery and assistance outside the UK may well not be at the same level expected!