You've got several issues here that need fixing. First you should have this table structure and relationships:
Events::EventID = Enrollment::EventID
Contacts::ContactID = Enrollment::ContactID
You should not include the other fields in your relationship as there is no need for this and won't make it possible for one person to be enrolled in multiple events.
To enroll contacts in an event, place a portal to Enrollment on your events layout. Put Enrollment::ContactID in this portal row formatted with a drop down list or pop up menu of ContactID's in column 1 and contact names in column 2. Selecting a contact from this list enrolls them in the event. A status field in the Enrollment table can then be used to record who actually attended the event if you need that data. You can place additional fields from Events in this portal row to show the name, location, date of the event if you choose to do so.
Here's a demo file that matches contracts to companies in the same type of many to many relationship. If you were to rename the two main tables "events" and "Contacts", it would match what I am describing here: