Hi, Grégoire. Thanks for getting in touch about your question.
Unfortunately, we don’t currently have built-in solution for pushing events to Facebook. Other users have expressed interested in this functionality, though, so if you wouldn’t mind taking a minute to check out our User Voice forum, we’d appreciate you joining the conversation there. We definitely prioritize new features based on user feedback in that forum.
I know it’s not ideal, but you might be interested to know that some of our users have worked around this by using our Eventbrite Tickets add-on, and pushing events to Facebook from the Eventbrite interface.