The most important thing is initially to get them onto your other half's attestation de sante. (It has taken us 2 and a half years to finally get the carte vitales but we had the attestations pretty quickly) The form you need for this is a 'Declaration en vue du rattachement des membres de la famille assures pour le benefice de l'assurance maladie et maternite' References on the form - top left CERFA No 12047'01 + bottom right S 3126a. This is what the RSI have just sent out to me after I tried to add Maisy (our 3rd child) to my husband's carte vitale.
We are insured with RSI Ram Gamex as my hubby is AutoEntrepreneur Prof Liberale. Kiddies 1+2 were born in France and have French extrait de naissance so were added instantly and a new attestation issued. Maisy however was born in England (hubby working in London at the mo) so adding her has been more tricky. Our top up insurance added her but RSI are messing us about so now I am getting letters from top up insurer asking why their records do not match RSI....I'm chasing my tail!
Anyway I've filled out the above form (which has possibly the longest name ever for a form) and it asks for a livret de famille which of course we don't have because we're English so I am going to send over Maisy's birth certificate translated into French and certified by our local Mairie for the second time - again with registered post (avec avis de reception).
If you are English I would recommend speaking to Newcastle Department of Health ASAP and asking for a form S2 (formerly E112 - permission to have your baby abroad) http://www.nhs.uk/NHSEngland/Healthcareabroad/plannedtreatment/Pages/Givingbirth.aspx this form will then mean you won't pay anything in the hospital as it would all be settled directly with the UK. You also have 2 options for all your other feuille de soins. 1. Send them to the UK to Newcastle to be reimbursed under your UK cover or save them and once you have the attestation de Sante then send them all in to the french system to be reimbursed, they should backdate the attestation to the date you moved to France with your husband. Make sure you save your ordanances (prescriptions) and if you have any medecines the vignette (little sticker) off the side of the packet needs sticking to your pharmacy ordanance.
When I had my first baby in France I was insured under the UK system and the french hospital didn't even ask for the S2 form but it was good to have it just in case. For my 2nd I was under the French system and just needed to give them the attestation de sante.
I know the pregnancy bit is expensive but just wait till you have the baby - monthly medecin visits & vaccin's add up too! I'm currently owed around 400 euro now because they are so slow at adding Maisy. Although I recall being owed over a thousand euro during my first pregnancy! It all came back eventually but the paperwork is almost a full time job! I think my other half has it easy going to work as he doesn't have to do all this silly nonsense!
Good luck & if I can be of any help, just ask :)