According to Wikipedia and io9, Zipf's law can be applied to "big cities" and agglomerates of big cities (e.g. San Francisco and Oakland). More specifically, according to the Wikipedia article, the power law fits with a factor of 1.07:
When Zipf's law is checked for cities, a better fit has been found with b = 1.07; i.e. the n-th largest settlement is 1/(n^1.07) the size of the largest settlement
A similar fact is stated (without reference) in this Nature Scientific Report.
However, I have yet to find any example where this law works in European cities. Here are some examples:
Belgium: Largest city has 1,019,022 inhabitants. According to the law, the three subsequent cities should have 485,379 , 314,531 and 231,195 people. This respectively corresponds to a 6%, 23% and 15% difference between the expected value and actual value.
France: largest city is Paris with 2,229,621 inhabitants. The Zipf's power law is off by 24%, 37% and 10% with respects to reality.
Germany: Berlin has 3,426,354 inhabitants. Zipf's power law is off by 7%, 17% and 20% for the three following cities.
Italy: Rome's population 2,318,895. Zipf with 1.07 factor is off by 11%, 25% and 40%.
Out of curiosity I have also checked it out for Mexico and it fails drastically as well: Mexico city has about four million people and the following four cities in population size are all about 1.5 million people. However, it does seem to somewhat work for the largest US cities.
Is there any evidence this law indeed works for the population of European cities? Subsequently, how about for other "big cities"?