Carte vitale for german traveilleur frontalier

Hello,

I live in Alsace and work in Germany. I have a private health insurance in Germany and I want to get a french social insurance number.
As far as I got it, I need to apply for a "carte vitale".

Is this right?
How can I do this?

Which kind of documents do you need from me and where to send them?
Please consider that due to my private health insurance I can't provide a "S1" standard form, this is only provided by the national state health insurance.

Thanks
michel126