I have a form developed with the Caldera Forms plugin, all site in wordpress.
Today the files that are being sent by the form, via upload, are sent as attachments in the emails. You would need the links, just the links, of each file to be uploaded.
The process would be, the files sent by the form, would be hosted on the site server, wordpress, normal, as is done today when uploading an image. And the link to that image would be sent in the form's email body.