Firefox is NOT an email client, so it will not open with Gmail, it will open as what it is:  a web browser.
If you want open Gmail automatically, go to Thunderbird and set it up the Gmail account.  You can use POP  (download mails to your computer, leaving the originals in the server)  or  IMAP  (synchronize all your folders and mails between server and your computer).  This is as you like it.
You will send and receive from Thunderbird  (and configure it as  "default mail program").




Hope this helps
Lailah