It seems I did not choose the best time to move my website. My new hosting provider is currently moving and cannot respond adequately to support requests. I have for example a strange thing going on with the DNS record of my mail server.
I would also have preferred using a PHP script to catch file not found errors. That would allow me to install a efficient cache system and to have better URLs. But after a week without response I decided it would be better launching the new website now than waiting indefinitely.
Today I reached someone who explained me what’s happening: the phone lines of their new support center are still not installed (installation planned for tomorrow) so support doesn’t work… I suppose what they mean by that is that internet is not accessible to the support staff. Bell is responsible of this delay apparently.
They have really good prices however. :-)