Firefox currently doesn't allow web pages to access the clipboard via JavaScript, so your only option would be to use the keyboard.

Does Shift+Insert work in case the website is intercepting the Ctrl key?

What kind of content are you trying to paste? Is that plain text or formatted content?

Use keyboard shortcuts if the buttons on the web page or other methods aren't working.

• Copy: Ctrl+C or Ctrl+Insert (Mac: Command + C)
• Paste: Ctrl+V or Shift+Insert (Mac: Command + V)
• Cut: Ctrl+X or Shift+Delete (Mac: Command + X)

Spaincentral said

Copying from another document and pasting into our SharePoint site - I receive the message that "Your browser is not configured to allow access to your computer's clipboard. Use Control+X for Cut, Control+C for Copy, and Control+V for Paste". However Control+V will not actually paste anything and I can't find any configuration setting in Firefox that can be changed.

Shift + Insert worked! Thanks so much!!