Just checked your site. The ajax response is fine - so the problem is in adding the events from the response to the calendar. (There's not clue here as to what is going wrong - there is no error message in the browser console).
Have you tried disabling other plug-ins and/or switching to TwentyEleven - this will identify/disprove any plug-in/theme conflicts.
Regarding the single event page, it seems that you using a custom template (i.e. there is a
single-event.php template present in your theme/child-theme). You can edit it there (as per this page) and use the available functions to output event details.
A couple errors I did get in the console (but shouldn't cause the issues you're reporting) were:
GET ... jcarousel.css 404 (Not Found) /calendrier/:32
GET ... ajax-loader.gif 404 (Not Found) /calendrier/:303
GET ... captcha.gif 404 (Not Found)
(nothing to do with Event Organiser).
Also, I couldn't right click anywhere...?