What are possible ways to implement such scenario? I can think of some Azure function which will periodically check the share for new files. Are there any other possibilities.
I have been thinking also about duplicating the files to Blob storage and generate the notifications from there.
Storage content trigger is by default available for blobs. If you look for migrating to blob storage, then you can utilise BlobTrigger Azure function. In case of file trigger in File Share, the below are my suggestions as requested:
A TimerTrigger Azure function that acts as a poll to check for new file in that time frame the previous trigger occured.
Recurrence trigger in logic app to poll and check for new contents.
A continuous WebJob to continuously poll the File Share checking for new contents.
In my opinion, duplicating the files to Blob storage and making your notification work may not be a great option, because such operation once again requires a polling mechanism which can be achieved with options like a few mentioned above, but is still unnecessary.