Equivalent le plus proche à ma connaissance.

Actually I would put this as List No. 3 instead of record no. 3. It is actually stating that it's a list of crimes committed the person committed. It shall be used as an exhibit against the person in any future offense and/or trial. It's considered as a list of convictions and/or all crimes person committed in the past.

From the French Consulate General in New York:
Criminal Records come in three forms (called bulletins).
…
Bulletin no. 3 This comprises only convictions for crimes and misdemeanors resulting in sentences of two or more years’ imprisonment, along with any current disqualifications or deprivations. It may only be issued…
http://www.consulfrance-newyork.org/spip.php?article355

From the French Consulate general in London:
How to obtain your "bulletin n° 3" :
You should personally contact the French ministry of Justice, "Service du casier judiciaire", who is the only relevant authority. The "Bulletin n° 3" (French certificate of good conduct) is issued free of charge to the person concerned only.
http://www.ambafrance-uk.org/The-French-certificate-of-good,...

FRANCE
Individuals can request their "Bulletin 3" record as an extract from the National Criminal Record by contacting the National Criminal Record Service at:
http://www.the-sia.org.uk/home/licensing/cctv/wizard/oversea...

EC-Council | LPT Police Verification AddressesAt Service public fédéral Justice Service du Casier judiciaire central Porte de Hal .... Relevant document – Police Criminal Record Certificate ...... Forms ‘Request for a bulletin No 3’ (Demande de B3) French citizens born on Mayotte ...
www.eccouncil.org/LPT-police-verification.htm - 599k -

Bulletin No 3 is the "extrait de casier judiciaire" which cannot be directly translated into English because it's a French legal term. The approximate translation would be French Certificate of Good Conduct.

http://www.justice.gouv.fr/index.php?rubrique=10017&ssrubriq...

http://www.ambafrance-uk.org/The-French-certificate-of-good,...

http://www.consulfrance-toronto.org/spip.php?article962

The French criminal record: "Extrait de casier judiciaire"
How to obtain your "bulletin n° 3" :

You should personally contact the French ministry of Justice, "Service du casier judiciaire", which is the only relevant authority. The "Bulletin n° 3" (French certificate of good conduct) is issued free of charge to the person concerned only.