The procedure is not the same as for French Social Security and a classic private insurance provider. The CFE does not transmit statements to insurers. In fact, with most insurers, it's the other way around: you send the invoices and medical reports to the insurer, who pays you both its share and the CFE's share. The insurer then sends an invoice to the CFE to be reimbursed for the amount it paid on their behalf.
With your preselected insurer (Assur Travel), the exact procedure is as follows: you send them your documents, they process then forward the documents to the CFE, the CFE responds to them with the amount it will reimburse, and the insurer reimburses you this amount plus the amount from your expatriate health insurance that makes up the difference. The whole procedure takes around 3-4 weeks.
Other insurers (such as ASFE and Humanis) reimburse before receiving the payment information from the CFE. This allows for documents to be processed a little faster (around 10 days), but does not change the procedure.
Reimbursements are made by wire transfer to accounts in France or abroad, in the currency of the account specified by the insured person. For most insurers, you can send your original invoices by regular mail, along with the claim forms that are found on their websites. In some rare cases, insurers will agree to reimburse you once they have received your documents by email. If you live in an area where mail delivery is difficult or sporadic, feel free to let your advisor know so they can take this into account when choosing potential plans.
For more information, please visit the following page: "How are reimbursements calculated for amounts not covered by the CFE?"
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