I have found some discussions about the peculiar demographic growth of France in the 19th century; this is a different approach to the same question.
I am interested not so much in the reasons why France grew so slowly, but in what would have happened if it had a similar growth rate to most other European countries.
From 1800 to the first World War the population of France increased by less than a half, from ~27 million to a mere ~39 million. During the interwar period it actually declined.
Imagine though a France of 50, 60 or even 70 million on the eve of World War 1; or even previously, in 1870-1871. I think there is little doubt that a different demographic reality would have had a tremendous influence on world events, wars in particular. A France on par with Germany would have weighted more in both a military and an economic sense.
Also, if France had, say, 60 million people in the 1940s, the OTL post-WW2 ‘miracle-growth’ would have resulted in a ~90 million large France today.