For my AF purchased via DL flights (some of which were JFK to CDG), I just checked in via my AF app and used the mobile BP to enter security. As a precaution, before boarding I'll stop by the GA for a quick document check, just to avoid the potential of the machine beeping during boarding. Ah, sometimes, most recently KE, texted me for a document check before boarding a flight from HND to ICN to the US. However, don't ever recall receiving such a text from AF, irrespective of whether purchased directly or via DL.

Never had any issues at JFK.