Is there anyone more obvious to manage him? If not, you may be stuck with him for now. It's hard on him, he must feel unwanted, but really, you are not the right role to manage him. I'd have thought HR in the absence of anyone else would be it. He might not be great at his job, but maybe that's because he's demotivated, not getting training or support where he needs it.
I would absolutely push back on doing facilities work when he's not in - it's a very different role from marketing. Our facilities do atuff like changing light bulbs, health and safety reviews, managing the door control passes, physical security reviews, supervising lift engineers and vending machine engineers, electricians and plumbers, coordinating first aider volunteers and the first aid boxes, workstation assesments and ordering of special support chairs, weekly fire alarm tests and scheduling evacuation drills etc. Many of these things require training (some of it just stuff like working at heights H&S training videos, but stuff like how the door control works probably has its own stuff,) which I mostly wouldn't expect someone in marketing to have, because it's not part of a marketing role...
I do not think you should be blamed for his incompetence, but I would look at what could be done to help him. Is he actually incompetent or just thoroughly demotivated by the company not giving a damn about him?
Have you asked him what he wants? Does he just want to plod along till retirement, does he want to do a good job if he gets support, and maybe progress in future? Is he incompetent because he's never had training or support? Is it the specific work tasks or more generally time keeping, reporting of work/paperwork, communication? Because some of the latter is down to more general management, and you could help him with things like better prioritisation, if that's an issue.
I would ask if there's some sort of procedure manual/work instructions - for him, not you. Does he follow it? Does it cover everything he's expected to do - regular tasks, problems, requests? If not, can he write a list of what's missing, and start writing instructions to fill the gaps? Does he need training in anything? Is there budget for it?
If you're in a union, ask them for advice. If you have an EAP, check what that covers - I discovered recently ours can include management coaching for things like difficult conversations.
(If I were him, I'd be looking elsewhere for work.)