The iPhone's lithium ion batteries are thought to be to blame
French consumer groups are investigating reports of iPhones that explode or crack spontaneously.
An 80-year-old from the Paris suburbs was among eight people who said their phones' screens were affected, according to the AFP news agency.
Consumers in the UK, Holland and Sweden have reported similar problems, prompting an earlier EU investigation.
Apple said it was aware of the reports and was waiting to receive the handsets from the affected customers.
The firm has been accused of trying to hush-up cases of iPhones and iPods heating up or bursting into flames in the US and the UK.
Earlier this year, Ken Stanborough and his daughter, from Liverpool, accused the firm of trying to silence them with a gagging order after the child's iPod exploded and the family sought a refund.
Apple reportedly offered to pay the money to Mr Stanborough, but only if he kept the terms of the settlement confidential.
It has been reported that the device's lithium ion batteries could be the source of the problem.
In the latest case, Rolland Caufman, a pensioner from a Paris suburb, said his iPhone screen had broken up without explanation in July, the week after he bought it.
"I took it out of my pocket and held it to my ear and saw the screen crack up like a car windscreen," he told AFP.
Mr Caufman has since been issued a replacement phone.
However, there have been other, similar reports.
On Tuesday, a 26-year-old security guard claimed he was hit in the eye with a glass shard when his iPhone screen cracked up.
He has said he would seek a full refund and file suit for damages.
The incidents have prompted investigations by French consumer affairs groups.
"An investigation is under way. We have been alerted to the problem and we are looking into it closely," said a spokesman from watchdog DGCCRF.
The European Commission has also asked the 27 EU nations to keep it informed of any problems, under its Rapex scheme.
Rapex is the EU rapid alert system for dangerous consumer products.
The system issue alerts for multiple products every week, sometimes leading to mass product recalls, but often with no consequence.
Apple, which has sold 26 million iPhones and 200 million iPods to date, said it was aware of the reports.
"We are waiting to receive the iPhones from the customers," said Alan Hely, head of European Communications for Apple.
"Until we have the full details, we don't have anything further to add."