Registration for free downloadable file

Hi,

There is no option to do that.
Free downloadable files are by essence free to download.
If you want them to require the customer to register, then, create a product with a price of 0 and don't set the files as a free download in the product. That way, the customer will have to go through the checkout (and register) in order to be able to download the files. If the total of the order is 0, there won't be any need for payment and with the "free order validate" plugin that you can enable via the Joomla plugins manager, your customer will be able to download the file on his order details page and his download area (if activated) and in the notification email sent after the checkout.