In my head, I hear "I've not seen that," with a stuffy British accent. :)
In Canada and the USA, I believe that "I haven't seen that" is more common, but both are correct.
The only time I can think of where "I've" is incorrect is where "have" is taken to mean "must". You can't say "I've to go" or "I've to take a sick day."
Funny...I originally typed "You cannot say..." and it sounded too British in my head. :P