Making Ctrl+C copy text in gnome-terminal?

You can change the keybinding for Cut and Paste from the default Ctrl+Shift+C, Ctrl+Shift+V to what you say, namely Ctrl+C, Ctrl+V, in the Edit → Keyboard Shortcuts menu. Though you should also change the default terminal meaning associated with Ctrl+C (interrupt), for example in this way

stty intr ^J

(I chose Ctrl+J because I don't remember it is associate with some action, but you can make your own choice.)

I don't think it is possible to retain the default interrupt action for Ctrl+C only when there is no text highlighted.

Ctrl + C is already assigned to another command, which is the one that interrupts the program that is running in the terminal For example, ping www.google.com will start pinging Google until you tell it to stop. The way you do it, is by pressing Ctrl + C

So, they couldn't just change the assignment of that combination.

Highlight the text you want to copy, press Ctrl + Shift + C and it is copied to the clipboard. Ctrl + Shift + V and you paste it.

Let me know if it doesn't work...

As already noted, Ctrl + C is typically used for interrupting a program. But instead of using Ctrl + Shift + C to copy, which I do much more frequently than interrupting a process, I change the setting to have Ctrl + C to copy and Ctrl + Shift + C to interrupt.

You can do this in GNOME Terminal by going to "Edit" -> "Keyboard Shortcuts..." and map the "Copy" action to Ctrl + C and "Paste" to Ctrl + V. The interrupt command will automatically be remapped to Ctrl + Shift + C.