I know that your character cannot hold two of the same legendary items (such as two Won Khim Lau fistweapons), but what about my follower? If I'm using a Maximus, can I give a second Maximus to my Enchantress, or will it tell me I can't?
Yes you can. I just tested this by buying and equipping 2 cheap uniques. Even though I could not equip both on my character, I was able to equip one and give the other to my follower.
I also tried to give my follower 2 of the same unique ring. He was only able to equip one of them, so followers also cannot bypass the unique equipped requirement.