English translation: True copy of an entry in the register of births
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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
French term or phrase:
Extrait délivré conforme à l\'acte de naissance n°
Explanation: I can only speak for the UK, but here the birth certificate is a certified copy of an entry in the register, rather than a copy of a certificate, hence my proposed translation. I've kept my confidence level at medium as my proposal could be completely irrelevant in other jurisdictions!