Many historians have attempted to explain this, even back in the late 19th century.

What we know is that fertility rates, which had been pretty stable for centuries (around 45 births for a thousand people), dropped after the Revolution, as low as below 30/1000 in the early 1830's and 22/1000 in 1900.

One thing that explains this drop is the Revolution itself. Dechristianization, a process supported by both the most bourgeois and the most radical revolutionnaries, meant that women could more widely make use of various contraceptive methods, that people had less incentive to get married and give birth.

While this new mindset was making its way among the population, France was hit by a demographic disaster: almost 25 years of constant war. On the first hand, it meant that thousands upon thousands of men were killed in distant countries. On the other hand, it meant many people willingly avoided having children, out of fear of seeing them getting drafted into the army and killed. This was especially common among the poorer families, who couldn't afford to pay a tax to avoid military obligations.

Meanwhile, starting at the end of the 18th century, life expectancy was quickly rising: from an estimated 25 years on average in 1749 to 40 years in 1830. People waited longer before getting married, and they didn't feel the need to have 5 or 8 children, as newborns would survive much more often than they used to (one children out of three didn't make it past his second birthday in the 18th century).

And while France's population stagnated (there were barely more births than deaths until 1860), other countries saw their population increase steadily. They also benefited from an increased life expectancy, but hadn't gone through the events that made French people have significantly less babies and wouldn't until the last quarter of the 19th c.

And you know what? France's elites were pretty much happy about this. The conservative bourgeoisie that was ruling the country was warry of the unruly crowds., that appeared with the industrial revolution, (later theorized by Gustave Le Bon in his "The Crowd: A Study of the Popular Mind"), had taken its intellectual toll, especially after three attempted revolutions (1789, 1830, 1848, and soon 1871). Reducing birth rates among the working class was seen as a good thing. It meant less insecurity, less poverty, less riots.

Then 1870 happened, France was crushed, in part because Prussia and her allies could mobilize more able men, and all of sudden, French rulers understood that France was no longuer the most populated country in Europe. This led them to set up a pro-natalist policy meant to catch up with Germany (and the UK). But it was too late: most French people had gotten used to having two or three children only.

TDLR, For various historical reasons, France's fertility rates started to decline almost a century before her neighbours'.

Sources : La fécondité française au XIXe siècle, Etienne Van de Walle Evolution générale de la population française depuis le XVIIIe siècle. J. Bourgeois-Picha