What CMS are you using? Most common CMS have plugins which will do a better job updating any non-HTTPS resources to HTTPS.
I know you requested no referral to another link but:
The Apache docs recommend against using a rewrite:
To redirect http URLs to https, do the following:
<VirtualHost *:80>
ServerName www.example.com
Redirect / https://www.example.com/
</VirtualHost>
<VirtualHost *:443>
ServerName www.example.com
# ... SSL configuration goes here
</VirtualHost>
This snippet should go into main server configuration file, not into .htaccess as asked in the question.
This article might have come up only after the question was asked and answered, but seems to be the current way to go.
https://stackoverflow.com/a/21798882/11039985
If you must use htaccess:
RewriteEngine On
RewriteCond %{HTTPS} !on
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI}
Update: per your response, after making a backup of the htaccess file and try:
Options +FollowSymLinks
Options -Indexes
RewriteEngine On
RewriteCond %{HTTPS} !on
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
RewriteCond %{SCRIPT_FILENAME} !-d
RewriteCond %{SCRIPT_FILENAME} !-f
RewriteRule . index.php [L,QSA]