It never ceases to surprise me, when monarchists claim the impossibility of restoring monarchies. The Romanian one is not an impossibility at all, but I will say that I see no way at all for the line to pass to any foreign member of the Hohenzollern princely family. They have no connection to Romanian society, the head of the princely family and his heir have made it clear that their family is not interested in the Romanian throne, and that Romania has a RF. Who and how succession will work in that family, can be sorted, and will fall into place, if the institution of monarchy continues to undergo its current renaissance.
If you want to invoke the EU in any way when it comes to the change from republic to monarchy in any member state, I think the most relevant intervention they would make, would be to make it clear that in this day and age, salic law has no place. And H.M the King of the Romanians has a more than large enough family to build succession around, when that day comes.
And I'm fairly sure it will. If you watch Romanian society closely, the winds are blowing in that direction.