In this case while you bought a DL ticket from DL, it is operated by AF, and therefore seat selection is an AF function.

As suggested, call DL and ask "for the AF record locator", which will be different from the DL record locator. Note that in the US, DL supports AF and therefore, you could ask to be transferred to an AF representative who can likely select your seat. However, I like to look at the map myself, which is why I recommend simply requesting the record locator and going online.

Next, go to AF.com and type in the AF record locator as well as your last name, and your reservation as well as seat selection should be available.