How to remove black adhesive from the windshield?

Take a single edge razor blade scraper and use it with a spray bottle of window cleaner. Spray on a light mist, then start at the top and work the blade under it. Keep working and spraying until it's off. The spray is to keep it from sticking back on and provides some lubrication for the blade. I prefer these style scrapers for this as they allow better control.
If you don't think you will need it again you can find them in many dollar stores or hardware sections in other stores.

If you use a sharp blade, you can remove all of it. No different than removing a registration or inspection sticker or other decals stuck on the glass.

Here is a video on the process:

https://www.youtube.com/watch?v=AP2E7soycRY

Googone would work on adhesive residue but that looks to be a plastic disc glued to the glass. As such the goo gone isn't going to work as it can't get to the actual glue.