Delta's press release on post-purchase upgrades includes this line:

only itineraries wholly operated by Delta are eligible for post-purchase upgrades, subject to availability.

https://news.delta.com/customers-now...anage-upgrades

Maybe there's an AF day-of-departure opportunity.

You might be able to upgrade DL-operated segments with miles: https://news.delta.com/buying-upgrad...-fly-delta-app