Why do you think there's a regulatory limit in the first place?

Because the people in charge are government employees.

An abundance of caution.

better a bit of caution than a slow and painful death?

If history is any indicator it's a good idea to be more cautious than less

I don't see anyone in this thread arguing against an abundance of caution. But an abundance of caution doesn't mean the "phones cause cancer people were right"

Yes, which is why the radiation limits for cell phones was set to 10x lower than the lowest amount that might be theoretically even slightly harmful.

Now one testing lab in France says that one particular phone is slightly (less than 10%) higher than those already very conservative, cautious limits.

Most likely scenario: the testing lab used the wrong methodology. This is what happened in France many times previously.

Also possible: the testing lab is right, some phones are slightly out of compliance. They're still safe. The radiation levels are still way below levels that are even theoretically harmful.

Because slow-cooking your brain is a bad thing?

Or maybe because possibly interfering the operation of other electrical devices, that have only been tested to operate with certain levels of external interference; is a bad thing!

This specific test is not about that: it's about radiation absorbed by the user during operation of the device.