If you provide the link or a similar one because you may not want to share it, we have more info. Chances are the website does not use the proper MIME type that Firefox relies on, unlike other browsers (that may be more susceptible to any tricks because of this. Additionally, you could quickly set up another [[Use the Profile Manager to create and remove Firefox profiles|profile]] to see what happens there, or have a look at the [[Applications panel - Set how Firefox handles different types of files]] and [[Change what Firefox does when you click on or download a file]] support articles. Look at the section that describes to remove the ''handlers.json'' file to reset the defaults in case that file is damaged. Then again, a new (test) profile will quickly indicate whether or not the issue is related to the website, or perhaps even your Linux distribution, its settings or additional (pgp) software?

Added AddType application/octet-stream .sig AddType application/octet-stream .pdf.sig to my .htaccess and the issue seems resolved. Not sure if FF still needs fixing though.