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The first thing you are going to have to do is look into OAuth2 for authentication this will allow you to access your users Google Calendars. You will just need to save the refresh Token for each user then you will be able to access the information again by requesting a new access Token.
After that you should look into the Google Calendar API reference
There is also a Google Client library for python that will probably make things a lot easer. Google APIs Client Library for Python.
I don’t have any django or python experience so I cant help you out with any code. But if you get stuck just ask a new question on Stack. These links should at least give you an idea of where to start.
Source:stackexchange.com