The French agency that regulates radio frequencies, the ANFR, said testing found that the model emits more electromagnetic waves susceptible to be absorbed by the body than permitted.
The ANFR said it "ordered Apple to remove the iPhone 12 from the French market from September 12 due to the model exceeding the limit" for electromagnetic absorption by the body.
It said accredited labs had found absorption of electromagnetic energy by the body at 5.74 watts per kilogram during tests simulating when the phone was being held in the hand or kept in a pocket.
The European standard is a specific absorption rate of 4.0 watts per kilogram in such tests.
"Concerning phones already sold, Apple must in the briefest of delays take corrective measures to bring the affected phones into compliance," said the ANFR in a statement on its website.
"Otherwise, Apple will have to recall them."
ANFR noted that tests that measure the electromagnetic radiation absorbed at a distance of five centimetres was in compliance with the limit of 2.0 watts per kilogram.
ANFR said its agents would verify beginning Wednesday that iPhone 12 models were no longer being offered for sale in France.
When contacted by AFP Apple did not have an immediate comment.
Regulators in a number of countries have limits on the amount of electromagnetic radiation mobile phones may emit to prevent adverse health effects.
The World Health Organization states on its website that following a large number of studies that "no adverse health effects have been established as being caused by mobile phone use".