This was not the end of my problems.
After having downloaded and installed ADE 2.0 using IE and got my PC authorization, I tried to execute a acsm file ( in fact a xml file) downloaded from my books provider site.
Then I got a connection issue with no more comment from ADE 2.0.
Then I right-clicked on the "Download" button on the provider site ( or on the option sent in the provider mail), copied it in a IE windows URL field and executed it, downloaded the acsm file and executed it by double-clicking.
Then I was able to get the Epub file.
After that all is working fine even using CHROME as default browser to download and execute acsm files.
To summarize:
To get ADE working on a Windows 7 with CHROME as default browser I had to:
1) uninstalled ADE downloaded and installed using CHROME
2) Download and install ADE using Internet Explorer
3) Download and execute a acsm file, using IE, just once
4) Then I can get Epub files using CHROME or IE
This seems strange, I would be interested by a technical explanation to avoid to loose 3 days more a next time.