Why should he have to give up his title? I would say him being a Duke makes it even easier. He is the head of the House, the relatives are all dead or not influential, no one can complain, so he can basically do as he pleases... of course if she is officially in the family records as his adopted sister that is a bit of a problem, but there are lots of solutions for it (for example having her again adopted by another family, especially since Eugene as lots of power and influence there should be families wanting his favor who would take her in officially) and it's not really something he has to give up his title for.
Does this have a novel? Who does she really end up with?? I'm so curious right now!!!!