The comparison with German is not going to be very helpful, in general. Here are rules of thumb for French:

1. All reflexive and reciprocal verbs are conjugated with être
2. Most of the rest of the verbs are conjugated with avoir
3. Except for a short list of verbs, which, when used intransitively, are conjugated with être

The rule of thumb for the short list is that they generally indicate some motion or movement. They are often assembled into a mnemonic diagram called “la maison d’être” such as you can easily find on the web (like here).

It is worth it to simply memorize this list since the same rules apply not only to Passé Composé but to all compound tenses.