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If you are the webmaster for that website, I suggest converting the movie to a different format, such as .avi and then reposting the video. Other wise, firefox cant install the quicktime plugin and cant play .mov files.
with that being said, if you are not t he webmaster, there is a change you can make to firefox internaly which may allow the video to play
In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.
(2) In the search box above the list, type or paste mp4 and pause while the list is filtered
(3) Double-click the media.mp4.enabled preference to switch it from true to false
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