Odd!
I clicked your link and got an ordinary http:// connection.
So I stuck an https:// in front and got what I take to be a secure connection (Chrome showed me a little green padlock).
Perhaps the SIA have staff dedicated to monitoring EuroGA, and fixed it within the hour?
I’m sure they have the budget… 
I had the same problem this morning. I got rid of it by switching from Firefox to Chrome!
Should the French CAA fire their IT chief?
Not necessarily – but if a more able candidate shows up, they might be interested. Said candidate would of course need to fill the prerequisites before being considered, and France being France, the prerequisite requirements might be much harder to meet than those on professional capacity. Not that it would be much different in my own country.
Works for me in Chrome on Debian and Safari on Mac OSX, but doesn’t work in Firefox (neither Debian’s Iceweasel rebranded Firefox nor Firefox-branded version running on Windows).
In my experience sometimes you can renew your certificate with your CA, the old one not requiring a certificate chain, then all of a sudden then new one does require a chain but the CA doesn’t tell you about it so you don’t realise you need to download and install a couple of other certs from your CA. You test it of course on browsers you have to hand and it works fine not realising it’s not fine on others until someone reports it to you.
This seems to be a bug in Firefox. Firefox does not allow self-signed security certificates anymore. Normally you get a warning but can add an exception and accept the certficate anyway. In the current version this option is missing.
There is a work-around for current Firefox. From memory, it is something like
Copy the exact URL to the clipboard
Options / Advanced / Certificates / View Certificates / Servers / Add Exception
and paste it in there.
I did it the other day for one private site.
I wouldn’t know about that, I don’t have any experiences of, ahem, “private” sites
It’s not a dodgy site 
It is one of great many websites set up for some business purpose where you want HTTPS but don’t want to pay 200 quid a year to Verisign or whatever – because the site will not be published. Actually you can nowadays get a certificate for free from e.g. StartSSL (in Israel) but for some reason that wasn’t done.
