How did it go?
They seem to have advertised quite a few posts and are interviewing before the application deadline.

A colleague of mine got almost exactly the same response. He is married to a non teaching spouse, has 2 children and does not teach a shortage subjetc. Search refused to sign him up... He got a job a couple of weeks later in a good school.
I'm in the same boat (and my spouse is not US or EU) and there was only 1 job I actually wanted this recruiting season and I got it (not through Search). If you're a fit, you're a fit! Keep looking and stay positive. Some schools prefer families as they tend to be more stable.
All the best!

OK, I understand (I think!)
Most British International Schools will only employ teachers with QTS (Qualified Teacher Status). You might want to research how to obtain QTS if you don't have it, there are a few different ways, the PGCE being one of them.
It is a tough time on the international scene at the moment because lots of teachers are unemployed in the UK and are applying overseas. Only Maths and Science seem to be in shortage...
Having said that, I've met some French teachers in British International Schools teaching French, Spanish, PE and Primary so again, good luck!

Christophe,
do you have the CAPES? If so you should look at the French schools abroad http://www.aefe.fr/
Most French teachers I know in international schools have a PGCE and trained in the UK, but I mainly know British International Schools. From your post, you seem to have trained in France so look at the French system!
There are also some francophone independent schools but they vary greatly in quality and the Belgian schools (in Kinshasa and Kigali)
Bonne chance!