It is actually a quite mysterious thing. France experienced a very unusual demographic transition in the 19th (from high birth + mortality rate, to low birth and mortality rate). Normally, the birth rate lowers years after the mortality rate but in the case of France, both rates declined at the same time.

http://en.wikipedia.org/wiki/Demographics_of_France#1800_to_20th_century

http://en.wikipedia.org/wiki/Demographic_transition#France

There are some theories as to why. One of them is that the Napoleonic code, that extended to the whole country the equality of inheritance between siblings (which was something that only existed in the Loire area before the Revolution) made peasants refrain from having lots of kids in order to divide their properties. It's not impossible: the aristocracy in the 12th century had a similar habit (low birth rate to prevent division of lands).