As you may know, there's a possibility to access files used by your Azure Function and stored by it by going to Platform Features -> App Service Editor in the portal:
It allows you to quickly browse what is accessible to your function and check whether everything is okay. Additionally you can even edit files if needed. However, what is an alternative to logging to the portal and accessing Function App by a browser? Fortunately, there's another way of doing this by using Azure Storage Explorer.
Using Storage Explorer
If you don't have Storage Explorer yet, you can easily install it from this link. Once installed, you can add a storage account used by a Function App to be able to browse its files:
Click on "Add Account"
Use storage account name and key
Enter account name and key
Once you have configured new storage account, it should be accessible from the storage account browser.
To access files stored by a Function App you have to choose a storage account you previously added and go to File Shares - it should display a file share names exactly as your Function App, which allows you to access files from the underlying App Service. From there you can easily access, download and modify them as you wish.
Note that this functionality is available only for "newer" Functions Apps since those created some time ago, didn't link itself to a file share.