Skyteam Elite Plus Members are afforded all the relevant perks whenever travelling on a Skyteam flight, subject to the usual provisos (lounge access requires (connection to/from) a same-day international Skyteam flight). It does not matter how the ticket was acquired or paid for.

As your status perks come from an FFP not noted on your ticket, carry your Delta status card to show your entitlement to, and to obtain, the relevant benefits