The thieves initially took four artworks, valued together at around nine million euros ($A14.5 million), but dropped two of them in the museum's gardens as they fled, Cagnes-sur-Mer mayor Bryan Masson said on Facebook.
"Attacking the Renoir museum is attacking a part of the history and heritage of Cagnes-sur-Mer. These actions are particularly serious," Masson said.
The museum was created in 1960 in the mansion of the impressionist painter Pierre-Auguste Renoir on a hill in Cagnes-sur-Mer, near Nice, where he died in 1919. The collection on display in the museum includes 13 paintings from the master and some 40 sculptures, furniture and photographs.
The stolen works included Portrait of Madame Colonna Romano, Coco Lisant and Young Girl at the Well, Nice-Matin newspaper reported.
Renoir's most valuable works have fetched dozens of millions of dollars at auctions in the past.
Art thieves in Europe are committing more violent robberies and specialist gangs have been replaced by ad hoc opportunists recruited through social media, pan-European police body Europol said last month.
The heist at the Louvre Museum in Paris in October last year was a prime example of this, Europol said, as the thieves threatened guards and visitors and stole 88 million euros worth of jewels, such as Empress Eugenie's tiara.
with AP
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