Whaow thank you so much Mr. Admin for your quick help!
My problem was tricky, I hope you'll not be able to reproduce it, or if it's the case, that you'll read this thread
In the <head> of your template 'index.php', it's important not to forget to insert <jdoc:include type="head" /> otherwise it will not work.
In my exemple it was included, so what? Haha, did you know that <jdoc:include type="head"/> is different that <jdoc:include type="head" /> ? Yes, the space juste before the slash! Think about it, because it can totally change the way your menu is displayed!