The problem might be from something that they eat.

Here is some information about US background radiation levels.

http://mtnweekly.com/radiation-levels-in-colorado-highest-in-world-16210

I have not found information on the background radiation in France, but there is information about the Chernobyl accident and its effect in various countries.

From:

http://users.owt.com/smsrpm/Chernobyl/glbrad.html

“The plume from the burning graphite initially traveled in a northwest direction toward Sweden, Finland and eastern Europe, exposing the public to levels up to 100 times the normal background radiation. A very serious concern involves the contamination of grain and dairy products from fallout. This contamination presents the chance for permanent internal contamination. Both Sr-90 and I-131 migrate to vital organs in the body where they are impossible to remove, serving as a constant source of unnecessary radiation and as a cause of cancer or other diseases.”