Zapier has a recipe that can do this.
I've just set it up and tested it and it seems to work well. It creates a new Facebook Page Event when a new Google Calendar entry is created.
So far, I've only got it triggering when a new event is created in G Cal, but it might be possible to get it to go through the G Cal diary and transfer existing events.
RecipeThe recipe is named "Create Facebook Page Event from Google Calendar Event" and is here: http://zpr.io/GDDa
Currently they have a free plan which allows you 100 tasks/month, running the recipe every 15 minutes. If you want more tasks or more frequent runs then they make you pay.
You have to give it (at least) read-access to the Google Calendar, and write access to the Facebook Page (obviously).