Bulletin 3 of the criminal record can only be requested by the person concerned or his legal representative if he is a minor or an adult under guardianship. In no case may it be issued to a third party, under penalty of a 7,500 euro fine (articles R.82, 777 and 781 of the Code of Criminal Procedure). 
if you are a French resident or citizen you can do you own Criminal record checks in France. I believe some unscrupulous persons do these checks by pretext - eg they use the personal information on the pretext they are the actual subject - name, dob, address etc. It is not to difficult, but I believe totally illegal. It is normally pretty useless information as it only gives convictions that receive a minimum period of 3 years imprisonment or more but I cannot confirm this at the moment. I have done my own CR check in France so I know the format but this was two years ago.
You can use a solicitor or as I know some French PI,s state they are the legal representative and do these checks. A PI,s is not a legal representative. Some websites claim they can get the convictions, as I said treat with caution and remember you will not get offences not treated as serious under French Law.
In order for our company to establish correct information on Criminal Convictions we can legally do this but you need to now an area where the subject has been legally resident and we research the court records. Takes time and is expensive but legal.
Attached is a copy of my License issued in France 2014 with a copy of the criminal convictions at the end of the document for you to see an actual document.
This is the link for the CC check in France available with English translation. CC Check in France 
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