Problem with CB Google Translate

Of course, here are the screenshots (attachments):

Strange, works fine in my tests. Likely a JavaScript conflict on the site causing the issue. Switch to Joomla's default template then retry and see if issue persists. If it does please PM a link to your site (link to PM me directly in my forum signature) and will take a look at the JS errors.

Good morning!
Indeed by changing the Template, with Pronostar, it works very well and the drop-down menu is there.
I'll PM you the address of my site if you ever want to look.
Thank you in advance.

Unfortunately it's a conflict coming from your template. There's nothing I can do about this. You'd need to try and find why your template could be breaking this. It seams to be messing with some of the page JavaScript. It's also possible it's a module or something else rendered on the page causing the conflict and switching templates prevented that module from loading. There seams to be some strange JS in the header referencing a plugin called plg_social2s.

Do you know what are the files (php, html, ...) related to the different templates that Community Builder could modify during the installation for the login module? This would allow me to compare the files of beez3 (my template) and protostar (template where the plugin works)

I disabled social2s and the problem is the same