You can carry on using the same socket code with GTK+, and use the socket file descriptor to monitor if there is any data arriving, disconnection etc. within GTK+.
Also GTK+ has a library called GIO that can also handle socket coding in an object orientated way and offers additional support for other things you may need such as TLS (SSL) support if you want to add a secure layer. It is also a portability layer, so if you want to port to another system then this should make things simpler.
Since this is probably your first GUI application, you should really read the documentation and tutorials first. Tadej has produced some very tutorials at http://blog.borovsak.si/
I would suggest designing your GUI using Glade. It is an application where you can place your widgets in your windows giving them names, and save the information as an XML file. This can then be recalled in your application to display your windows and if you need to recall individual widgets by name. This should ease some of the learning needed and allow some flexibility in the design. With GTK+ you can choose many languages or use the native C API.