This is completely wrong. I did that countless times, including very recently. You can select seats but if you want to select the correct one, you need to go on the site of the carrier operating the flight. So if you have an AF-operated flight (whatever you have a ticket with an AF or a DL flight number), you go on AF (or KL) web site. Same logic if DL-operated flight, go on DL web site.

On AF site, you need the Amadeus reference (as I don't think it's recognizing DL booking ref). On DL web site, you can use indifferently Amadeus ref or DL booking ref.