I had no problems getting into the AF business lounges in Berlin and Paris with my PM/CRC card. The staff first looked up the kinds of acceptable lounge cards in a loose-leaf folder, and there was the DL card!
I've always been well treated on AF, even when on a DL ticket, in business, on the Concorde, and in Y class. I never had the impression that their staff were treating me any better or worse than an AF member. They put all business-class passengers in the same hotel when a flight was cancelled, gave us all first-class amenities kits when baggage was not on the same plane, gave me the seats I requested when making reservations, and were even unfailingly polite and pleasant (yes, even that!). Their customer service office in Florida answers complaints quickly and even offers vouchers for future travel when there is a problem.
KE treated me very well as a DL PM in their business lounges, at the gate and on board, albeit while on a DL-issued Skyteam, business, round-the-world ticket. Ditto with Aeromexico.