AF and DL are close enough partners that they can actually pull up each other's reservations electronically. Even so, I recommend bringing a copy of the onward itinerary to show the check-in agent so they can get the baggage interlined properly. I find paper is convenient, but you can also usually just hand your smartphone to the agent; the information on the itinerary is usually all the agent needs to get it set up for you...

Note that, since you last interlined bags, Delta's rules have gotten much more restrictive about which partners they'll send bags to across separate tickets. The list is pretty much only "airlines Delta has a joint venture or financial interest in". In your case, that's fine because AF is on the list - but keep it in mind when planning future travel. https://pro.delta.com/content/agency...-policy--.html