I remember that the coins in Bellatrix's vault (Deathly Hallows) were cursed with the Gemino and Flagrante charms. Those were probably special coins which were permeable to such magic. What stops the normal Galleons, Knuts and Sickles from being duplicated? Is it mentioned anywhere?
I don't know what, if anything, stops Gringotts coins from being duplicated.
Wonderbook (walkthrough), a video game with spell descriptions written by J.K. Rowling, gives some detail about the Gemino Curse:
The Doubling Charm. Don't get too excited, none of the duplicates are actually worthy anything. [...] The Doubling Charm has caused trouble from its discovery. Many disputes have arisen around the question of whether a copy created b the Gemino Curse is of equal value to its pair. As the two are identical at first it is impossible to know, although the copy usually rots or tarnishes much more quickly.
So even if you could duplicate Gringotts coins, they wouldn't be useful for very long.
I would be unsurprised if there were special enchantments to prevent forgeries, duplicate or tampering, but I don't know of any canon sources which confirm that. (Perhaps it's impossible to prevent duplicate, in which case maybe they just modify the coins to accelerate the decomposition.)
I don't know what, if anything, we can draw from the coins in the Lestrange vault. They could be real wizarding coins – the Ministry and Gringotts don't seem to raid prisoner vaults, as evidenced by Sirius's hoard – or they could be a historical hoard of Muggle coins, as the pure-blood families rubbed shoulders with the Muggle aristocracy before the Statute of Secrecy was imposed.