I think I discovered a bug !
This theme I’m using allows me to have 3 menus.
After an update, it appears that the flags appear ONLY if there is already a content in the menu.
Before, I used to use the third menu for the language purpose and it was able to show only the flags.
So for now, I added a “Language” item in my 3rd menu to make it work, but I wonder if you could help with that ? It was looking more “clean” to have only the flags.