Benjamin,

I think there is a more positive news for you.

As you were flyig F accross the pond (I assume LH) you are allowed to use the FCT in FRA (or any F lounge) and the SEN lounge in CDG. It is in one of hte satelites (BTW the 1K will do as well). The question is if it is worth it consideringthe distances.

I am not sure how the Air Madrid / LH location /transfer is in CDG.

On the interline it is a clear yes.

My experience is that they do it. Especially if oyu ask nicely.

I once had it that they somehow couldn't do it in the system, so they wrote the tag mannually and then put the tag numers for the LH flights into the system.