Unfortunately I don't remember how to remove/disable read more that you already have in File Catalog but I do know how to add the one where you want it.
I can't really tell from screen shot if you wanted the "Read more" after Comments or Stars.
So in this example I will show you how to add it after Comments
Go to CP » Customize design » File Catalog » Appearance of entries
Find this code:
<?if($COMMENTS_URL$)?>| <a href="$COMMENTS_URL$">Comments ($COMMENTS_NUM$)</a><?endif?>
and paste this code after it:
<a href="$ENTRY_URL$">Read more</a>
Save it and your done.