Yes, there is a Catholic remnant in France.
But even in the heyday of the Church there, France had a singularly bad reputation. His Most Christian Majesty usually had a half dozen children out of wedlock, at least. Louis XIV probably had hundreds.
When there is no official statistic (and there isn't) the plural of anecdote is data. One sees it all over France. Of course, the data will NEVER exist, because France isn't going to make official racial distinctions among Frenchmen. Still, there have been private samplings, published in the various media, and the trends are good. I will see if I can find some and post them to you.
I would like to see some polling data that might help establish the trends in birth rates you claim. No scientists can accept a collection of anecdotes as anything other than anecdotes. Indeed, some very nefarious projects have relied on anecodates and not solid statistical data. While sampling is better than nothing, the best data are complete census data. Everything is subject to greater error.