I am in the process of applying for a Junior professorship in Germany (see also this earlier question here. If the job listing is in German, and does not explicitely state a language requirement, should the application be in German, or can it be in English? Further, does the same apply to the required "CV"?
Unless stated otherwise, you should apply in German.
Most undergrad courses are taught in German, and usually it is expected that your German is good enough to teach in German, and also good enough to write an application in German. You may check the departments website if they have any courses in English, and if you even find that they offer a degree where everything is taught in English you may consider asking the contact person (see the job ad).