The 320-bed facility in Oloron-Sainte-Marie near the Pyrenees mountains was hit by the attack on Monday, with screens displaying a demand in English for $50,000 in Bitcoin.
Hospital workers have had to revert to working with pens and paper, since digital patient records are not available.
The management system, used to monitor medicine stocks and other supplies, has also been affected at a time when the hospital is taking part in vaccination efforts against Covid-19.
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“We might get our systems back in 48 hours or in three months,” hospital director Frederic Lecenne told local newspaper La Republique des Pyrenees.
He said personnel had disconnected some computers from the internet and the hospital’s network to try to limit the spread of the ransomware.
In February, hospitals in Dax in southwest France and in Villefranche-sur-Saône in the southeastern Rhone region were subjected to ransomware attacks, while in 2019 a hospital in northern Rouen was also hit.
“Ransomware” attacks see criminals infiltrate and paralyse a target’s IT systems, then demand payments in order to restore them.