Create a Google Calendar event with an attachment in Apps Script

Code.gs

function createEventWithAttachment() {
  var driveFileId = '...';
  var file = DriveApp.getFileById(driveFileId);
  var event = {
    summary: 'Test Event with Attachments',
    description: 'Woot!',
    attachments: [{
      fileId: driveFileId,
      fileUrl: file.getUrl(),
      mimeType: file.getMimeType(),
      title: file.getName()
    }],
    start: {
      dateTime: '2016-02-18T17:00:00',
      timeZone: 'America/New_York'
    },
    end: {
      dateTime: '2016-02-18T18:00:00',
      timeZone: 'America/New_York'
    }
  };
  Calendar.Events.insert(event, 'primary', {
    supportsAttachments: true
  });
}

Make you you've enabled the Calendar advanced service and have toggled it on in your Cloud project.