Yep, Jones is right.
As for controlling audacity, nothing can do that except your mouse. You can record with it, but that’s all it really is, a recording tool that has production tools with it. It’s not dj software by any stretch of the imagination.
Basically, it’d go: Mixer hooked into your soundcard to your PC, with a timecode box (there’s quite a few out there for Serato & Traktor), with the CDJs going into the timecode box.
I know you can record mixes & such with Audacity, but due to every single proper software having a record function now a days, using audacity to record your mixes is outdated unless you’re using a hybrid set up. As for recording to your CDj, that’s also not possible. The CDJ is just a reader & control surface, not a recording device.
Best of luck!