OK. Problem disapeared this morning.
In fact, I am not sure I totally exited the game yesterday. I could call back my FC and am now on board. Not sure what happened there.
I also had a detailed look at my logs, and seen that I was hunted by several PNCs before being shot.
As there was only 1 pirate and 3 security services, I conclude that I probably inadvertently shot at security forces.
It's the only way I could explain that.
So, I'm back in game now.
Thanks all for your insights and advice.
I edited the initial post accordingly.