Stressing this was a precautionary measure, the ANSM regulatory agency urged people to return all boxes of Furosemide Teva 40 mg to their pharmacists.
The agency suspended sales of two batches of the drug last Friday after a pharmacist reported sleepiness in a patient.
Prosecutors opened a probe the following day after the death of a nonagenarian in the southern city of Marseille. A box of the pills from one of two contaminated batches was found at the patient's house.
The agency did not specify which one of the patients, nor why it linked the other person to the case.
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"Other reports are being investigated," it added.
The agency urged people to return the medicine to their pharmacist "as soon as possible" -- regardless of the lot number, to be replaced by another brand.
Furosemide Teva 40 mg is a diuretic used to treat water retention in people with congestive heart failure and disorders of the liver, kidney and lung.
France has had a series of medical scares since it emerged domestic company PIP had produced breast prostheses containing industrial-grade silicone gel.
An estimated 300,000 women in 65 countries are believed to have received faulty implants.