DL 8548 Checkin CDG
 

I believe that the Delta/Air France counters are one in the same (as part of the JV, AF/KLM covers local ops in CDG/AMS and Delta covers them in the US) so it doesn't really matter here.

But for when that is not the case, you always check in with the operating carrier, not the marketing carrier (so Air France in this case).

You'll always check-in with the operating carrier. Doesn't matter what your flight number is at this point. As far as I know, this holds true regardless of airline, alliance, country, etc. On day of departure, it's the airline flying the plane that controls everything.

You will check in at the SkyPriority zone in Terminal 2E. It is roughly in the middle of the terminal. You will need to show your "SkyPriority" itinerary (iPhone screen is fine) to the agent at the entry area to gain access. Two hours prior to flight time should be fine, but if you want to ensure time to visit the lounge and not be stressed, I'd suggest three.

I would plan on 3 hours, check in and Immigration at CDG during the morning rush even through the SkyPriority line are crowded and slow. Look for check-in zone 6-7 or the big red SkyPriority banner.

CDG doesn't have "Delta" check in counters. They are all Air France / KLM / SkyTeam. They will understand "Sky Priority". You may find some of the lanes for security and such labeled as "Access 1". Your Sky Priority mobile boarding pass should give you access to these lanes. Security / Passport control can be hit and miss (more often miss) in particular if you are not using an EU passport that qualifies for the automatic passport kiosk ("Parafe"). French immigration scans all passports on exit.

As a general rule: At the airport, you always check in with the airline operating the flight, not the airline you purchased the ticket from. In many airports it doesn't matter since the counters tend to be next to each other or "blended" like in CDG. But in other airports it can matter a lot (e.g. AF / Delta use different terminals in JFK. May still work to check in at a Delta counter but I doubt it).

In theory you have to check in with the operating carrier in this case, but in practice I've got a BP from the connections desk at JFK T4 and then proceeded to T1 security directly. Could be because the precedent flight was on the same ticket and a BP could not be issued when checked in for the first segment. But if the itinerary is originating at JFK I highly doubt DL will do the check-in at T4 even if it's on a DL codeshare.