Why has France had a slow increase in population compared to other Western European countries, especially during the Industrial Revolution?

There are several interesting reasons for this, and it is still a hotly debated topic among historians. Here are a few theories.

France ran against Malthusian limits much earlier than other Western European countries. The population simply could not expand without adopting newer agricultural techniques, which only happened later on.
Related to 1, France's traditions of passing down land (every son gets some v. only the first son getting it in Britain) caused land to constantly be subdivided into smaller and less efficient plots. This helped ensure a far too small supply of food for a growing population.
New population patterns and industrialization entailed having fewer children than say, Britain. Without more cities absorbing excess peasantry, the peasants in France used different techniques (celibacy, infanticide) to control the population. In Britain, excess children would be absorbed into industrial production.
Differences in lifespan. This is probably the most contested one here, but there's some indication that French lifespans during the Industrial Revolution remained more stagnant than those in Britain.

It's important to remember that the population of France did grow tremendously - just less dramatically than Britain or Germany. Demographic history is a very difficult subject to get a handle on, especially considering the difficulty of obtaining records from the time. For more information I'd recommend A Short History of the Industrial Revolution in Britain (which contains a lot of comparisons with France), Barbier's Scarcity and Frontiers, Weber's Peasants into Frenchmen, and Malthus' works on human populations.