Angus, for those Smart Matches to be correct.
1) Franz and Mina would have to be TWINS (not otherwise mentioned)
2) Franz and Mina would have to have been born as TWINS and OUT OF WEDLOCK (to a woman who would later be Maximillian's second wife) ON THE SAME EXACT DATE that the legitimate son, Karl, was born to Maximillian's wife.
I think it is much more likely that someone simply copy-pasted the dates of birth wrong, putting Mina and Franz onto Karl's birth dtate and thus making it seem that Maximillian had a bigamous relationship that produced three children born on one day!
Also, the other record i found online (which i entered into the comments field) of Maximillian's record) has Anna dying some time after the birth of her fourth child, then Maximillian marrying to Cecillle after about three years and then having two children, not twins, with Ceccille, his second wife.
(Smiling at the idea of the very proper Herr Heinsheimer with three newborn babies in his arms and two wives on their childbirth beds and a puzzled look on his face!)