NOTICE: WhatsApp Web is now compatible with Firefox! You don't need to install this addon any more
This addon removes the checks WhatsApp put in place to disable Firefox accessing the WhatsApp Web interface. By installing this addon, these checks will get bypassed, so accessing https://web.whatsapp.com should just work. From personal (and limited) testing, WhatsApp Web works just fine on Firefox.
If there are issues, please let me know by opening issues on https://github.com/elopez/enablewhatsappweb/issues
This add-on is open source, you can get its code from https://github.com/elopez/enablewhatsappweb. It is heavily based on @h4writer's "enable Google Inbox" addon, thanks @h4writer!