Hi Jean-Philippe. Thanks for your question. The Facebook Events Add-On imports Facebook events as WordPress Events. It does NOT publish WordPress Events to Facebook.
(By “WordPress Events”, I mean the event posts created by The Events Calendar.)
If you want to share your website’s events to Facebook, just post a link and Facebook should take care of the rest (displaying an image, event description, etc, depending on what information you added to your event).
I hope this information helps in your decision to use/purchase The Events Calendar and its valuable add-ons. Let me know if you have follow-up questions.