My understanding of the rules is that since you are CO Platinum and CO is still officially in Skyteam (at least for now), and CO Platinum is Skyteam Elite Plus status, and DL is a Skyteam member, and the DL flight is international in nature.....

You are entitled to complimentary access to either the AF or KL lounge (or both if you choose).

This is provided that the KL and AF lounges are operated by AF/KL and not subcontracted lounges. Subcontract lounges (such as TLV or BOM) don't count.

If you search around on the CO website under Skyteam Elite Benefits, you would find this little gem:

SkyTeam Partner Lounge Access: Platinum Elite members traveling in Economy Class enjoy complimentary access to most SkyTeam partner lounges worldwide. Simply present your same-day ticket for an international SkyTeam airline flight. As a OnePass Platinum Elite/SkyTeam Elite Plus passenger, you can even invite a guest to join you in the lounge.