try 2nd hugo config file

hugo_config/_default/theme_settings.toml

@@ -1 +1,3 @@
+[params]
+  background_color_class = "bg-purple"
   bg-color = "rouge"

static/admin/config.yml

@@ -42,4 +42,4 @@ collections:
         file: 'hugo_config/_default/theme_settings.toml'
         extension: toml
         fields:
-          - { label: Couleur du thème, name: bg-color, widget: 'select', options: ["rouge", "bleu", "vert"] }
+          - { label: Couleur du thème, name: background_color_class, widget: 'select', options: ["bg-red", "bg-blue", "bg-green", "bg-purple"] }