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 :
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.