Hi Nicolas,
Just received a first order on my new site, but found the order was in "cancelled" status, customer contacted me. The order was using Paypal. I never have this problem in old site, and even was tested on my new site before this order through my own Paypal account.
I have some order status created, not sure these effected, please see screenshot:
My Paypal setting:
My Checkout setting was as usual, but just let you have a browse:
Your response asap is much appreciated and sorry for trouble you again !!