@Biju Mathew Thank you for reaching out.
You can create a timer triggered Azure function that runs periodically, checks the file share, and updates the list of files to a table in your database.
The stored procedure can then consume from the table instead.
Yes, you can achieve the same using Azure Data Factory as well.
Do let us know if you have any further questions.
----------
If an answer is helpful, please "Accept answer" or "Up-Vote" for the same which might be beneficial to other community members reading this thread.