A local Paris newspaper reported that the robbery was interrupted by a police officer who was on patrol, yet still, two of the assailants were able to escape as they drove away on a motorised scooter.
Three men have been arrested, police said, while others remain on the run.
"He had an axe in his hand".
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Another put the figure at 4.5 million euros ($NZ7.5 million), but said that a bag had been recovered possibly containing some of the loot.
One hotel employee told the AFP news agency: "We heard a loud noise and lots of racket in the street".
The five-star Ritz Hotel is located in Place Vendôme, in Paris' historical first district on the right bank of the river Seine.
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Security in the area was increased in 2014 after several luxury jewellers were raided in violent robberies. The 19th century hotel, which reopened in 2016 after a four-year renovation, has housed such famous names as Ernest Hemingway and Coco Chanel.
A police auto is parked in front of the main entrance of the Ritz Paris where a burglary happened on Wednesday.
The hotel was bought in 1979 by Mohamed Al-Fayed, whose son Dodi was also killed in the fatal crash.
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The Ritz was the last building Princess Diana and Mr al Fayed's son, Dodi, left before their auto journey that ended in tragedy under the Pont de l'Alma on 31 August 1997.