Cron runs in an environment that knows nothing about the display manager (
$DISPLAY isn't set). Your terminal window that you've been testing in has this set for it. If you tried it in a "real" terminal, or over SSH, you'd see it break.
If you've only got one X server running, just specifying the display might work:
* * * * * DISPLAY=:0 firefox ...
You could probably put more effort into working out what display it's sitting under rather than assuming it's
:0 but that will probably work most of the time.
If you just need to reload something a lot, look at Tab Auto Reload or similar Firefox plugins.