The current release of Brackets-Git requires the very latest version of Brackets, which is newer than the latest Edge Code. Looks like version 0.13.18 of the extension is the latest version that supports Brackets 0.38, which is what Edge Code Preview 7 is based on. The extension registry stores older versions of extensions for precisely this version. Version 0.13.18 of Brackets-Git is available here: https://s3.amazonaws.com/extend.brackets/zaggino.brackets-git/zaggino.brackets-git-0.13.18 .zip.
If you need to do this in the future, just visit the Brackets Extension Registry online, find the extension there, copy its download URL to the clipboard, and then modify the version number part of the URL when pasting it into the "Install from URL" dialog. (To figure out what version is compatible, look at the history of the extension's package.json file to see which version lists 0.38 or lower as the minimum required Brackets version).
Hope that helps!
- Peter