There is FileChooser::browseForMultipleFilesOrDirectories and FileChooser::browseForMultipleFilesToOpen, but no way to ask the user for a list that is restricted to directories only. I added it to my own fork in about 5 minutes, but would be nice for it to be in JUCE proper. 
Did you consider opening a Pull Request? Or could you share your code so someone else can open a Pull Request?
Apart from getting the tabs wrong in the .cpp file, it’s here and otherwise correct. Saying it takes 5 minutes is probably over-estimating; copy/paste of the browseForMultipleFilesOrDirectories method minus the canSelectFiles option, it doesn’t seem worthwhile of a PR, plus I’m still not entirely clear on
We don’t accept third party GitHub pull requests directly
This only works correctly on macOS, it’s not currently possible with the native Windows or Linux file browsers which is probably why the method is missing from the FileChooser API.
Damn. Thanks for the info.