DEMO: https://forms.gle/2iPYvRuh3kxmCcFK6

Booking Calendar is an add-on used for Google forms. It permits the form's respondents to book the appointment from the form admin's Calendar. 

The add-on auto loads the events from Calendar under the rules that were set by the admin. It also adds the respondent as an attendee of the appointment slot that was booked by him.
It's easy to configure but very useful.