Having reviewed evidence of the effects of electromagnetic waves on children under six-years-old in specialised literature from around the world, Anses experts recommend that parents limit their children's access to digital equipment.
Electromagnetic waves may affect the congnitive functions of very young children, whose bodies and brains are more sensitive to them than those of adults, the report finds.
So it recommends limiting their use not only of phones and tablets but also of remote-controlled toys, such as cars, trains and cuddly toys, robots, walky-talkies and babyphones.
And intensive use of mobile phones affects their general well-being, although the agency attributes this to overuse rather than electromagnetic fields.
The report calls for more work to be done on reports of cases of depression and suicidal tendencies due to overuse.
But a lack of studies means that Anses could not reach a conclusion on digital technology's effects on children's hearing, development or reproductive and immune systems.
No figures for mobile use by under-sixes in France are available, although smartphone ownership by 12-17 year-olds leapt from 22 percent in 2011 to 55 percent in 2013.
The agency repeats its 2013 recommendation to both children and adults of "moderate use" of mobile phones, the main source of electromagnetic waves because of the strength of the waves they emit and the fact that they are placed directly against the ear or another part of the body.
But they have ruled out the implementation of a ban on allowing under-sixes from using mobiles, a measure that was approved by the French parliament in 2010 but has never been written into law.