Short answer: NO!
First off, hello my fellow coffee friends!
You cannot bring an electric coffee maker on your cruise with you. It will, and should, get confiscated. It is a fire risk.
I cannot speak to french presses, this is something you should call your cruise line to inquire about. It would be possible to get hot water at the lido or order it for room service. If you hear something about this, let me know so I can update this post!
There are a lot of coffee options on the cruise. Some are free, others are paid.
My advice is to bring your own travel coffee mug because those mugs are SMALL.
ProTip: try some soft serve in your coffee for an extra special treat. It is my must have on a cruise! C knows not to say anything as I sit there with two cups to pour more hot coffee in the ice cream.