OK. So I finally chatted with the help desk...
- They asked me to remove and re-install the software (that's a classic one).
- Then they asked me to download a couple of e-books from http://www.adobe.com/products/digital-editions/eBook.html and to open them.
As both steps above worked, they told me I had a problem with the .acsm file so they could not help further...
But re-downloading and opening it directly from the online shop where I bought the ebook worked... Finally...