Okay, so this one is not a folk tune, but it is one of my childhood favorites (we had it on cassette tape!)
It was originally a poem written by one of our most famous poets, József Attila (1905-1937).
A music group named Kormorán put it to music for their Christmas album in 1985.
And this one even has an official English translation! I am copying it from this site.
Kings of Bethlehem (English)
Little Jesus, God bless Thee, God bless Thee,
Royal kings we are all three.
Above us shone a blazing star,
on foot we’ve come from very far.
A little lamb so surely said
that Jesus Christ lay here in bed.
My name is King Melchior.
Help me, help me, my dear Lord.
Good day to you, Son of God, Son of God,
Silly old priests we are not.
News of your birth has travelled far,
King of the poor we’ve heard you are.
Hence our little visitation,
heaven’s kingdom’s our salvation.
My name’s Jasper and I think
I’m a kind of worldly king.
Greetings to you, Saviour, Saviour,
Our land is much sunnier.
All our sausage we have eaten,
our fine boots look weatherbeaten,
six handfuls of gold we have got,
also incense in a big pot.
King Balthazar, yes, that’s me:
The Saracen of the three.
Flushes-blushes sweet Mary, sweet Mary,
little mother she’s happy.
Casting down her eyes she peers
at her Jesus through her tears;
hear the shepherds’ music-playing,
feeding time bears no delaying.
"Kindly three kings make your bow,
I must bid you farewell now."
1976, Hundred Hungarian Poems, Albion Editions, Manchester
(Note: In the last verse, the Hungarian language is more direct: instead of 'feeding time bears no delaying' it actually says 'it is time to breastfeed [the baby]' which I always thought was very cute - Mary kicking everyone out because it is boobs time)