On Monday, French Socialist MP Yann Galut proposed an amendment to French law that - if passed - would see the US companies punished if they didn't give French officials backdoor access to terrorists' phones.
In France last year, there were eight phones that were inaccessible to police - all tied in some way to terror attacks, reports Le Parisien.
Galut said on Monday that companies like Apple and Google should be fined up to €1 million when they didn't cooperate in such cases.
"We are faced with a legal vacuum when it comes to data encryption, and it's blocking judicial investigations" he told Le Parisien newspaper.
"Only money will force these extremely powerful companies like Apple and Google to comply," he said.
Galut added that such companies were operating under "total bad faith".
"They are hiding behind a supposed privacy protection, but they're quick to make commercial use of personal data that they're collecting," he said.
He stressed that his proposed amendment would not affect the privacy of the common public, only those who are under investigation.
The case comes as Apple is embroiled in a legal battle in the US after a judge ordered the tech giant to find a way to unlock the encrypted iPhone of a gunman in the deadly San Bernardino shootings.
At a tech conference in Paris last week, Google chief Sundar Pichai expressed his support for Apple in its standoff with the FBI, warning that creating so-called "backdoors" into encrypted communications could have "bad consequences".
"We want to take a very strong stance against any form of backdoor whatsoever," Pichai said during the conference at the Sciences Po university, reported AFP.
"When you create backdooors it leads to very, very bad consequences which always ends up harming users."
Apple has won the backing of a number of Silicon Valley firms in its legal fight, with Facebook's Mark Zuckerberg saying Monday that he was "pretty sympathetic" with Apple's quandary.