For a fee, the FBI can provide you with your Identity History Summary Check, known as a rap sheet.
Please visit the FBI’s website for detailed information on obtaining an FBI background check: https://www.fbi.gov/services/cjis/identity-history-summary-checks.
More information on fingerprinting services.
You should confirm if the French requesting agency requires the results of the background check to be translated to French and/or affix the Apostille on the document for authentication purposes.
More information on Criminal Record Checks is available on the State Department’s website https://travel.state.gov/content/travel/en/international-travel/while-abroad/criminal-record-checks.html
The U.S. Embassy is not authorized to respond to private requests to collect fingerprints from U.S. citizens for law enforcement or other purposes. Although local police stations may be able to assist you with your fingerprinting needs, we have been told that many do not provide this service. Since it is becoming more and more difficult for U.S. citizens to obtain fingerprints overseas, U.S. citizens considering moving to France are advised to obtain prints in the United States before departing, or while returning for visits.
Getting your fingerprints taken: U.S. embassies and consulates do not provide this service. Please see: Fingerprint Identification: An Overview.
More information on fingerprinting services in France.