After Cortez and his men took control of Mexico City, they put together a package of spoils to send back to the Emperor. Gold, Montezuma's cloak, slaves, stuff like that. The Spanish ship got captured by a French pirate who then turned it all (?) over to the king of France, who then bragged to the Spanish Emperor about it.
Do any of those things still exist?
I unfortunately cannot confirm if any of these "bones of giants" are still extant in some museum, but the remains were almost certainly those of mammoths, whose fossils are abundant in Central Mexico.
If you're interested on that topic, you can read my own past comment on Did Native Americans have any interaction with dinosaur fossils? as well as the comment from /u/drylaw on Bones of giants, described within the memoirs of the conquistador Bernal Diaz del Castello.
In addition to the answers kindly linked by /u/400-rabbits you could also check out this earlier one, where I trace the path of this treasure via the French pirates and on to France:
I also haven't found much about its whereabouts now (difficult a couple centuries later). But if you're interested there's a great article on what happened to some other important Aztec artworks that were brought to Ambras collection in modern-day Austria: The Aztecs at Ambras: Social Networks and the Transfer of Cultural Knowledge of the New World by Mark Meadow, online here,
According to Meadow, Moctezuma's feather headdress and some other items had made it to Vienna in the 16th century, to Archduke Ferdinand II's Ambras Kunstkammer where some still remain - see here for more info on and pics of these Aztec featherworks.
The question of restitution of many prehispanic and colonial-era artifacts and sources from European countries to Mexico is still very current, by the way.