The “well-dressed and polished” couple and two children, speaking with French accents, pulled off the subtle heist at the Currado jewellery store late on Wednesday afternoon, the Milan edition of Corriere reported.
The family gave the impression they were serious customers, the newspaper said, with the parents “handling and trying on jewellery” while the children distracted the shop’s staff.
“Nobody noticed a thing,” the newspaper said, until the thieves were lost in the crowds of the Piazza del Duomo and the sale’s staff realised the pricey jewels had gone astray.
Police are now examining surveillance footage to try and catch the thieves.
Earlier this month, a woman in Turin was caught by police with €75,000 worth of diamonds and designer watches hidden in her bra.