What should I replace this broken condensate line connection with?
That is a simple brass hose barb.
I'd carefully unscrew it from the pipe, being sure not to twist and damage the PVC. Then I'd take it to my local hardware/big-box store and purchase one in a matching size.
If you have enough slack in the tubing, I'd also cut it off an inch or so below where the barbs are stuck in it and bring that to the store. I'd use it to ensure the barb end of my fitting went into the tubing.
If you don't have enough slack in the tubing, and, based on that angle and the fact that the brass fitting broke, I think you may not, I'd either:
A) Buy a short run of tubing and another double-barb fitting to patch the two together, or
B) Buy enough tubing to run to wherever this is supposed to go, but without stretching quite so tight. i.e. buy an additional foot or so more tubing than you currently have to relieve the strain on the fitting.
If you don't have any, pick up some white Teflon™ thread tape while you're at the store.

Put 1-2 twists of thread tape around the threads of the fitting (wrap clockwise, just like you'll screw the fitting in.
Tighten the brass hose barb into the PVC fitting (make sure you cleaned out all the old thread tape first). You'll want to tighten it firmly, but not over tight. Check back later for leaks (since this is a condensate drain) - if you see any leaking, give the fitting another 1/4 turn or so until the leaks stop.
Push the new hose onto the new barb end.
Connect the new section of hose to the old section with the double-barb connector (if necessary).