I make the trip a few times each year and found the following to be my best options:

DL from ATL to CPH, and then either SK to ARN. If you buy your ticket in advance, you can get a one-way from CPH to ARN for around $60.

If it's too expensive, you may want to consider the train from CPH to Stockholm. Runs every hour and takes about 4.5 hours... Cost: again, depending on how far in advance you buy your ticket, can be as low as $30... Check out www.sj.se

My backup is BRU and then Brussels Air to BMA. BMA is the smaller airport in Stockholm, closer to the Center... I think I paid about $90 r/t last time I got an ID95 on them.

As you may be aware, the days when you could show your pass card at AF and get on a flight are long gone... The agreement was replaced by an ID96 agreement a few years back. Sounds like a good deal, but it ends up just as expensive as an ID90 on some of the other airlines.

Also, try DL from JFK to TXL, and then Air Berlin from there to Stockholm. They have excellent rates sometimes...

Lots of options... Let me know if you need more ideas