It seems that the only fare class that DL has for intercontinental First Class is F, which maps to Air France's F fare class. Therefore, if the Air France flight is only selling tickets in P, you won't be able to book the DL codeshare.
You can use ITA Matrix to search and then BookWithMatrix or ITA PowerTools to book it, but the availability should be the same as Google Flights.
Yep, looks like AF is mostly P1 or P2 and F0 on their flights. Even when there are flights with F bucket available, AF11 JFK-CDG 3/30 for example, I wasn't successful in pulling it up on delta.com (Google Flights does not even have link and ITA Powertools/Bookwithmatrix tricks didn't work and Delta.com has no column for FC). It does appear possible to book DL codeshare on Priceline though.