How to sew a ripping zipper back on
It looks like the zipper tape has frayed, so there's not much left to stitch to. I think the best course of action would be three steps:


Stabilize the fraying zipper tape 
Reinforce the fraying zipper tape
Re-stitch the coat fabric to the zipper tape


There are a few ways to tackle #1. I'd probably douse the frayed zipper tape in a significant amount of Fray Check, especially right around the area near the teeth just where the fraying starts. Then, dig out your mini iron, take some fusible web (Heat n Bond) and iron it to some woven fabric to make some stabilizer, or get some medium-to-heavy iron-on interfacing, and iron it to the fraying parts (and about-to-be-fraying parts) of the zipper tape, to reinforce them with extra strength before you try to re-stitch the zipper to the coat.

I'm afraid that if you try to stitch it as it is now, there's not enough zipper tape to hold your stitching, and it'll pull right out again.

Good luck!