Parece que o Java está bloqueado no Firefox de 64 bits.
De: Blog Mozilla: use o plugin Java para visualizar conteúdo interativo em websites
Mozilla plans to drop support for all NPAPI plugins except for Flash in March 2017, when Firefox version 52 is released.
Note: The 64-bit version of Firefox does not recognize or support this plugin.
Também em Fóruns do Mozilla: sem plug-in Java
Mozilla/5.0 (Windows NT 6.1; Win64; x64; rv:43.0) Gecko/20100101 Firefox/43.0
You have the 64-bit version of Firefox, where only Silverlight and Flash Plugins are 'whitelisted'. If you need Java you need to install the 32-bit version of Firefox. You can have both the 64-bit and 32-bit versions installed, but you'll need to do a "custom" installation (on the first screen of the installer routine) and select or create a uniquely named folder - like maybe Firefox 32, otherwise the 32-bit installer may overwrite your 64-bit Firefox installation.
Isso se deve provavelmente ao esforço contínuo para erradicar o inseguro e o NPAPI plugins baseados .
Do ponto de vista de segurança, isso é Uma coisa boa (tm) , mas do seu ponto de vista você precisa usar uma versão de 32 bits do navegador.