I bet he will attend the Regina Apostolorum Pontifical University, the university of the catholic order and mouvement Regnum Christi, whose clergy members are known as Legionaries of Christ. There is a master in ethics in english also at statal Rome universtity, but I think that it has not the prestige to attract a stranger prince (and the course probably starts in september) ; the pontifical university, on the contrary, certify you that you're studying the catholic church point of view and that make a sense of going to Rome. The movement is thought to be quite conservative. And at this point we can't exclude a religious vocation for Felix as this movement is very capable in inspiring such vocations to royals (Paul of Austria, Alexander and Elena of 2 Sicilies, a Lobkowicz, a de Merode,...)
The site of this University is quite bad but I have understood that students can follow the program all over the year or in an intensive way (4 weeks : 1 in October, 1 in November, one in March, one in April for example...I can't remeber the correct months)
Finally: what a delicate topic to study for a Luxemburg prince!!