After reading several topics, I finally solved my issue thanks to this one (outdated, but it worked for me). For some reason, things are not always as easy as they seems.
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I added some packages to my installation :
chromium, libx11-6, libx11-data, libx11-dev
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And the following line at the end of the server.conf file :
report_disable_sandbox = true
After restarting the graylog server, this part works flawlessly.
Hoping that this post will help other people, thanks for your help !