I cannot find the link, but at last year's CanvasCon I asked this question in the Google Partner group forum and was told that the Google Apps (Classroom, etc) are not supported in the FFT accounts. The Google Apps link that you can find in the search in external tools in FFT is a depreciated service, so will not work. There needs to be ADMIN support for the service, and it is not one that is currently offered for FFT accounts. You can see the explanation for the new Google API Service that was just updated on May 21st.
Individual users can link their own Google Drives to their accounts for submitting assignments. you can see more about that HERE
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