Hi Muriel,
I've checked your site and it seems like you have assigned a default category with the category that has restricted permission for most of your user group thus causing the issue. I've change the default category to use "Actualité" and it should be working now.
EasyBlog - Showcase Module does not appear
I've checked your homepage and the module did appearing correctly as you can see from my screenshot here,
http://screencast.com/t/TsJchdziNBh . Am I missing something here?