I'm skeptical of before 19th century population counts, especially pre renaissance. Many calculations were done by modern local historians, not by same period sensus, who had strong bias in making their country more populous therefore looking more prosperous.
I wonder if sizes of armies through centuries can tell us the true(r) picture.
France army before WWII - 5 million (Germany 4.3 million, similar numbers for British)
During Napoleonic campaign, 130 years before, European powers had armies counted in hundred thousands. Napoleon's troops had 300,000 french people going to Russia. I would say that for this time period, size of armies fluctuated between 100 and 500 thousand, depending on time, need and country.
Granted that it was cheaper and easier for France to conscripted and transport more men in mid 20th century, than in much poorer France of beginning of 19th. To produce rifle and uniform for example is 5-10 fold more affordable in industrial era. I guess it wouldn't make sense for Napoleon to call for another 200 troops if there was not enough weapons and logistics for them and his army was already the biggest in Europe.
Even considering economics of weapon production I wouldn't guess that population of France wasn't much bigger than 10 million in 1800s.
There is even a bigger contrast in size of armies of middle ages, compared to later times. Battles were fought with single digit thousands and tens of thousands men. Granted that weapons and logistics were even more expensive in poor Middle Ages, and populations must have been much bigger, than I could gather from ratio of population to army size of 20th century.
I would estimated population size of middle age France to be around 2-4 million, and not 7 to 16 mil as per sources below.
http://en.wikipedia.org/wiki/Demographics_of_France
Likewise population size of France at year 1800 is given as 30 million, and 40 million (the only figure we can be sure of) by 1930. It means just 1/4 demographic increase through the most of industrial era!!! Mind that industrial times brings factory made fertilizer (nitrogen and potassium) plus new machinery which doubled and tripled food production in this time period, plus the climate got warmer too. By this way of understanding it would make more sense if population of France went from 10-15 million in year 1800 to 40 million in 1930s. Should we even mention improved hygienic, longer life span and lesser child mortality of 20th century?
Maybe I'm missing widespread birth control technology/pills of 19th century France. It is the only thing which could explain very slow population growth through industrial times.
And yet we have faster population growth in last 60 years (during birth control use) than in whole 130 years before.
PS. I just had a thought that perhaps biggest factor is the child mortality thing in general population statistics.
These days almost every kid survives till adulthood, but it was almost in reverse in middle ages. By some scientific estimates only 40% and in bad times as little as 20% of kids lived past age of 20. It means that we need 5-10 kids per family to sustain population number. It also means that at all times 80% of all citizens are kids, considering short lifespan of adults too. In today's France kids till age of 20 consists 25% of population.
1930 - 40 million total - 30 million adults
1800 - 30 million total - 10 million adults
Middle Ages - 10 million total - 2 million adults (1 million men, therefore armies of tens of thousands make sense)
But I still don't get how come demographic of France is so stagnant during industrial revolution?