I recently flew NWA from DTW to FRA and then Lufthansa to Dresden. The counter personnel in DTW knew exactly what to do to Interline it through to Lufthansa, HOWEVER I had to do a "transfer check-in" in Frankfurt to tell Lufthansa that I was there and was really going on my next flight. They couldn't do that in Detroit. Since you are arriving in CDG a day later than you leave, odds are you will have to also check in with AF when you get there. Make sure they see your luggage tags and scan them in to ensure your luggage will also arrive. Not sure what AF's policies are regarding transfer, but I imagine similar to Lufthansa's, so you should ask as soon as you get there.

Coming back I had discussions for 45 minutes with Lufthansa personnel who said they couldn't Interline my luggage, since "NWA isn't a partner in Interline." What rubbish, they said it was luck that it worked from DTW to Germany... After talking to 2 different managers and then making them call Lufthansa's international booking line from the counter they finally "agreed to make an exception" and check my luggage through to DTW, but that was probably just Lufthansa being Lufthansa. Hopefully you won't have that problem, just be aware that it IS possible and demand that they do it correctly. Like I said, you shouldn't have any problems in DTW.