Just to follow up, I was able to book the following itinerary on Delta.com. DL marketed flight numbers in La Premiere (booked into F fare class for the long haul segments, J for the short haul segments)
LHR-CDG-JFK-CDG-FRA
Interesting. I’ve done this a couple of times, but could never get the DL flight numbers if the flight went beyond CDG. Delta would only sell the La Premiere with its flight number that way, and it was “F” class. I tried onward connections but it vetoed out the F class on the CDG-LAX segment every time.