My last product, initially targeted at graphic designers, found a sweet spot with small business owners that struggled with FTP and who were looking for a drop-in replacement for their FTP server and file sharing needs.
I think the better question is:
Who shares large files with people? There's a group who deals with pain.
(one to one) Take a look at yousendit.com Sure, the title states FTP replacement, but I would bet that most people don't have an idea about what FTP is (my graphics designer didn't - but uses this service)
(one to many) - dropbox.com - easy file sync between geographically distributed people. easy to use mac and PC clients. freeimum.
Now - what would the benefit of using your product be over these services? What advanced feature set would these big file sharing types want that neither of the above support?
I would start with companies who sell FTP servers. Here's a list. Simple FTP servers are free, so if you're selling FTP servers you're serving a market of people who really care about FTP.
Next question: Who are they selling to? Answering that will take manual digging, but look at things like:
Banks, insurance, travel industry.
I would say any business that handles very large databases and needs to transfer them.
Enterprise software support and customer-facing development teams need a tool like this -- every team I've worked with (at big companies as well as smaller companies) either uses an FTP server or a one-off solution for securely sharing files with customers. You might try to reach out to the Agile development community and users of web-based Helpdesk/CRM tools if your product integrates well with the needs of this user base.
Sounds like drop.io can work for ya.
Motion Graphics companies