Depending on whether it is Delta metal, you could even manage the booking straight from your Delta app. Otherwise just install AF app and change the FF number there after you added the booking. Or call customer service, they are also able to do it. Or on AF website: many ways.

NB: to enjoy the ST elite + benefits you don’t technically need to add your Medallion number, but it is going to make things easier since your boarding pass will show SkyPriority and you won’t need to explain to non-alliance staff at airport why you should be able to use fast track based on your status etc etc. It is all directly tied to your boarding pass and turn stiles etc will/should automatically recognise it.