Well, I haven't made a purse, but .... my suggestion would be that a heavy-duty interfacing would be helpful (I have used some that are really stiff, like for use in corsets that would be great). If you don't have that available to you (I found some at Wal-Mart of all places!), I'd try plastic canvas that is used for needlepoint. It's flexible, but stiff enough to hold its shape. I hope these suggestions help you.
(BTW, the purse in your avatar is really cute!)