EDIT (October 18, 2017): Since the Windows 10 Fall Creators Update, you can now press the default F11 to access the Microsoft Edge full-screen mode.
A lot of regular Edge users and Windows Insiders have been requesting a full-screen mode for the Edge browser since it was first introduced. Unlike other browsers (and non-UWP apps) pressing F11 doesn’t activate a full-screen mode in Edge. Microsoft has been aware of this request for a long time.
*However, with no official word from Microsoft, it has come to light on Reddit that there is a full-screen mode in Edge and other UWP apps. Just press Windows key + Shift + Enter.
Microsoft Edge full-screen mode Keyboard Shortcut
F11 – Full Screen
Microsoft UWP app full-screen mode Keyboard Shortcut
Windows + Shift + Enter – Full Screen
*Thanks to onmsft.com for the heads up!