Medieval europe with a king and a girl peasant works wonderfully with me :)

As far as the selection process goes, it would depend on how he wants to be perceived. If he's not too worried about how they view him, he could make a decree and force it, as you said, all eligible maidens. Or if he was worried about it seeming more legit, as a kind gesture thing, he could make it a voluntary thing where he gussies it up as a beauty competition where he can watch and choose that way, or as a ball where he can mingle and interact and choose the one he likes best that way, then he comes off as more of a generous entertainer sort (also, if they are afraid of him, you still might get people going anyway in hopes of not catching the king's eye, but of either enjoying the evening or snagging a husband of a higher class than themselves). Third option to try to keep it in a positive PR light would be to have one of his men go searching and when he thinks he has found the right one, to make some sort of deal with the family in exchange for her so that there's no big public disturbance over the matter, keep it more of a quiet deal.

So... yeah, it speaks to his character and motives which route you'd go with it.