how do i cancel a tgv reservation?

I assume you mean tgv-europe.com rather than tgv.com. (They are separate sites). Here's a quote from the tgv-europe site: To apply for a ticket refund for one of the following reasons: •Ticket not received •Unable to print ticket •Cancellation Contact us at the following address: TGV-europe.com Service Clients BP 10012 B-1060 Bruxelles 6 Belgium Include with your application: •Your 6-digit booking reference. •Your original train tickets. •A photocopy of your bank statement showing this purchase.
•Your full contact details (full name, address and phone number)

What about canceling for another reason (eg, illness)

Sherry, I doubt that tgv-europe will ask why you want to cancel a reservation. People have lots of reasons for doing so.