My bet is, this is the last typo I need to fix.

tasks/configuration.yml

@@ -7,7 +7,7 @@
     src: files/config.json.j2
     dest: /home/hedgedocs/hedgedoc/onfig.json
     owner: hedgedocs
-    groupe: www-data
+    group: www-data
     mode: 0644
 
 - name: Configuration du fichier SystemD
@@ -15,7 +15,7 @@
     src: files/hedgedocs.service
     dest: /etc/systemd/system/hedgedocs.service
     owner: hedgedocs
-    groupe: www-data
+    group: www-data
     mode: 0644
     handlers:
         - Reload systemd