Good afternoon Arnaud and welcome to the Events Calendar Support forum!
Thank you for reaching out to us.
We are sorry to hear about the issue you are facing when people are trying to purchase tickets.
I would love to help you with this topic and, if you prefer, we can continue this conversation in french.
From what I am able to see, the issue seems to stem from the fact that you require people to login to purchase tickets.
Could you try removing that option under Events -> Settings -> Tickets and see if that helps ?
Best regards,
Geoff B.