I am going to leave the original answer below because it may be important for others that search for this question.
In short there doesn't seem to be a one size fits all answer, but with 'set clipboard=unnamedplus' one of either '*p' or '+p' should work from the "system" clipboard.
'*p' is almost certainly the one you want. (from here)
vim is a cli program. When using it inside gnome-terminal (or any terminal emulator) crtl+c (or any key combination) is handled by the terminal emulator first, then the shell, then finally by the program (vim in this case). vim and ctrl+c will almost certainly never work because ctrl+c sends an SIGINT signal to the running task. vim uses SIGINT to stop other things like aborting insert mode, or stopping search functions.
In other words. Ctrl+C is never actually passed to VIM. SIGINT is passed to VIM. SIGINT has other uses in vim so using to copy is likely not going to work (and even if can you force it, not a good idea).
Instead try sticking with Ctrl+Shift+C and Ctrl+Shift+V (there are others but I believe those put text in the system clipboard)
To be fair I don't know much about gvim.