Hi!
I realized I had not replied to this yet - sorry for this!
Just to tell that your advice worked perfectly, thanks a lot 
.
I overwrote the CMD of the filebeat image by just putting an empty string into my docker compose:
version: "3.3"
services:
filebeat:
image: docker.elastic.co/beats/filebeat:6.4.0
volumes:
- ./logs/:/usr/share/filebeat/logs/
# [...]
command: "" # to overwrite the -e that disables logging to file!
And it logged into file like a charm.
(Here are the possible flags / options to pass in that CMD / command: https://www.elastic.co/guide/en/beats/filebeat/current/command-line-options.html#global-flags)