Pretty much any argument you can use for FullCalendar can be plugged in here, with the notable exception that an argument with square brackets will break, because of how WordPress parses shortcode arguments.
The defaults that the plugin uses can be found in pgcal.js line 56: https://github.com/lbell/pretty-google-calendar/blob/d7a9738b60099b32df7b9ce7b99889380bdfebb1/public/js/pgcal.js#L56
Anything you put in fc_args will override or supplement those arguments.
So, for example, you can tweak options like the fixedWeekCount for the day grid, or specify your own headerToolbar.
Check out FullCalendar docs for some options: https://fullcalendar.io/docs
