How to step down gracefully I have a tenure track position at a European university. Owing to some serious health issues in my family I will move to be closer to them. 

I will resign before the term is over (but will try to keep on 1 day/mo to contribute to a small project and hopefully keep my title, I’m about to be promoted to Full Professor but I’m not sure how the faculty will react once they learn this). 

No one knows this. 

What’s the best way to move forward to preserve my relationship with the faculty?
Assuming you have a good relationship with the faculty at the moment:

I would discuss the situation honestly with your head of department or other appropriate person. It sounds like you have a good reason to want to be closer to your family. It also sounds as though you genuinely want to maintain links with the university. Those are reasonable goals, and if your department values you they will try to support them. Maybe you can keep a day or two a week, maybe you can work remotely, maybe you can visit for a week every two months... hopefully you can explore options and find something that works for everybody.