"The attacks took place overnight at 4am. Our teams have been at work since this morning," said a spokesman for Free, internet and mobile phone service provider, according to AFP.
In a message on Twitter, the company referred to "multiple malicious acts" targeting its cables.
Competitor SFR said it had experienced "several fibre cuts" in the Paris region and in Lyon in southeast France.
Other operators such as Bouygues Telecom are not affected because they use different networks, but problems were reported by users around the country including in the cities of Strasbourg and Grenoble.
The source of the problem is unknown at this stage, but experts stressed that apparently coordinated cuts to fibre optic cables were unprecedented.
"This sort of incident at this scale never happens," one security source said on condition of anonymity. "It's the first time and we don't know who it is for the moment."
KI/PR