a) There's a time-lag of probably 1-2 weeks between someone becoming infected, until their case hits the official statistics.
b) There will be different rates of testing between different areas, healthcare systems, and countries, which will be hard to quantify.
c) There will be fundamental differences between countries (e.g. patterns of population density, quality/availability of healthcare, etc.) which mean that direct per capita comparisons (as you made) are of little value.
Denmark's case number has increased far more than that of other countries in recent days. They probably had to act as they'd overtake Italy in less than a week with cases/capita if growth continues like that.
The case #'s only go up if you test more people. In Ohio for instance they are only testing very few people and there is now evidence of community spread because the 4th person confirmed had no known contact but you basically need to be in intensive car to get tested or have an obvious connection. So the case # in and of themselves could vary based upon testing criteria. Not sure if they have the same standards in Denmark vs France.
