It would be so simple if he simply made her a mistress, but this does seem late Victorian times so that was sometime looked down on, depending on the country.
Nevertheless, he is becoming a Duke, the highest position under a king (archduke is more like a minor king inside another kingdom) and that makes the hierarchical steps between him and the maid huge.
Even if he finds a trick, she is never going to be able to relax. She will be ridiculed by higher society constantly, and by the servants, everyone will be mocking her, giving her the stink eye, calling her vixen and not a single thing a single Duke can do about that.
Hell, I wouldn't be surprised if legitimate attempts on her life will be in order. Plenty of unscrupulous folk that desire to be bound to a dukedom's riches by finding a replacement marriage partner for him.