Creating an Audit (server or database) requires two things:
1.  An Audit definition at the server level (Server->Security->Audits) which defines *where* the audit will be saved (File, Application Log, or Security Log)
2.  A Database Audit Specification that defines *what* is going to be audited, which points to the Audit definition for where to be saved.

If you set the Audit Definition to point to a file location, you need to ensure that the SQL Server service account has Full Control (you could also try lower privileges such as Modify and Read) to the location in question, or SQL won't be able to create the audit files, and the audit fails.