Not only is the policy clear, but in this specific case, OP's second ticket is on AF to CDG. AF handles customer service for both DL in Europe, just as DL does this for AF in the US. Thus, the entire issue about what to do if the bag is not properly delivered is irrelevant.

When you check in at LAX, ask to have the bag checked to CDG. Have a printed hard copy of your e-ticket receipt for the onwards flight in your hand and give it to the check-in agent. Less room for error.