When the carte vital is not accepted at a hospital (ex. american hospital), we have to send the document "La feuille de soin" to the social security office by ourselves to get refunded.
General instruction of La feuille de soin
http://www.ameli.fr/assures/soins-et-remboursements/comment-etre-rembourse/la-feuille-de-soins_paris.php
Where to send?
http://www.ameli.fr/assures/votre-caisse-paris/nous-contacter/envoi-de-vos-feuilles-de-soins-et-courriers_paris.php
General instruction of La feuille de soin
http://www.ameli.fr/assures/soins-et-remboursements/comment-etre-rembourse/la-feuille-de-soins_paris.php
Where to send?
http://www.ameli.fr/assures/votre-caisse-paris/nous-contacter/envoi-de-vos-feuilles-de-soins-et-courriers_paris.php