Thank you for your help.
In fact it was due to the fact that my site is not installed on / but on /site_directory/
By adding those lines in the .htaccess, it solves the problem and now everything works like a charm 🙂
https://preventdirectaccess.com/docs/pda-rewrite-rules/
===
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /site_directory/
RewriteRule ^index\.php$ – [L]
# Prevent Direct Access Rewrite Rules
RewriteRule ^private/([a-zA-Z0-9-_.]+)$ index.php?pda_v3_pf=$1&pdav3_rexypo=ymerexy [L]
RewriteRule ^wp-content/uploads(/_pda/.*\.\w+)$ index.php?pda_v3_pf=$1 [QSA,L]
# Prevent Direct Access Rewrite Rules End
# IP Block Rewrite Rules for Folder Protection
RewriteRule ^wp-content/uploads(/(paid-members)/.*\.\w+)$ index.php?pda_v3_pf=$1 [QSA,L]
# IP Block Rewrite Rules for Folder Protection End
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
