A sample analysed on 28 March showed radioactivity levels of 8.5 becquerel.
In parallel testing, the French Institute for Radiological Protection and Nuclear Safety (IRSN), the national public institution monitoring nuclear and radiological risks, found iodine 131 in milk.
According to the institute, concentrations from a sample collected on 25 March showed levels of less than 0.11 becquerels per litre.
In normal times, no trace of iodine-131 should be detectable in rainwater or milk.
The rates detected are said to be extremely low – particularly in comparison to rates observed after Chernobyl in 1986 – and the authorities are stressing that there is no cause for panic.
Nevertheless, according to CRIIRAD, contamination of the air, and consequently of rain water, will continue for at least the next two weeks.
The independent body noted that the fallout of radioactive iodine-131 could reach several hundred becquerel per square metre – or even a few thousand Bq/m2 in the case of adverse weather conditions, for example.
Spinach, salads and other vegetables with large surface areas are among food products that are particularly sensitive to iodine-131 contamination, if they are cultivated outside and exposed to rain water.
Indirect contamination of milk in particular normally occurs within a couple of days if cows have been outside eating grass, CRIIRAD noted.
The fact that France's IRSN found iodine-131 in a milk sample taken on 25 March indicates that radioactive fallout has already been reaching Europe since at least 23 March.
Radioactive iodine-131 is particularly toxic when absorbed by the thyroid, where it saturates and leads to an increased risk of cancer.
When contacted by EurActiv the European Food Safety Authority stressed that the agency is not involved in measuring radioactivity, but remains vigilant and ready to provide technical assistance if requested.
The European Commission's department for energy, with the support of the EU's Joint Research Centre, is coordinating the EU executive's response to the alarm.
Its energy department is also responsible for legislation concerning radioactive levels in food and for introducing, if necessary, a safeguard clause to impose radioactive tests.
On 25 March, following evidence that the feed and food chain in Japan was affected by radiation escaping from the damaged Fukushima plant, the EU decided to reinforce controls on imports of food and feed from certain regions of Japan.
The Greens in the European Parliament note that EU limits on the maximum permitted levels for radiation in imported foodstuffs are "far less strict" than the limits that Japan itself is applying for internal consumption. They are calling for the immediate strengthening of the thresholds.