Additional note: I tried to follow these instructions (linking the libnpjp2.so) but then the JRE test crashed firefox.
Thanks to this page, I got the solution.
Using the JRE x64 rpm mentioned in the question, without icedtea plugin, all you need to do is linking the JRE library to firefox this way :
ln -s /usr/java/jre1.7.0_05/lib/amd64/libnpjp2.so ~/.mozilla/plugins/
In fact I just copied it the first time this is why it crashed. After that you can verify the plugin is installed in firefox by typing in the url :
And Java(TM) Plug-in 1.x will show up, no need to restart firefox.
Try to use icedtea plugin.
You installed java on your system, but you probably don't have the needed plugin in firefox.
In arch that plugin is icedtea, and as i can see, it also is in fedora: http://fedoraproject.org/wiki/Features/IcedTea