Is it true that in the 1860s only 20% of the French population regarded themselves as French, or spoke the French language?

20% would certainly be far too few for the 1860's, but this site indicates that in 1789, a good 50% of the "French" couldn't speak the language we now know as standard French, they spoke their regional tongues, some of which Baloo has mentioned. Quite likely, they would have thought of themselves as "Breton" or "Gascon" or something else, not French.

However, the influence of conscription under Napoleon was apparently signficant in terms of demanding a common language, and urbanization, industrialization, and new technologies for communication would have been influential as well over the course of the 19th century. French education laws in the 1880's then completed the task of ensuring that all the French could communicate with one another:


https://en.wikipedia.org/wiki/History_of_French

In his book "Peasants into Frenchmen. The Modernization of Rural France 1870-1914" Eugen Weber claims that in 1863 just 20% of the French population regarded themselves as French or spoke the French language.

As late as 1863, government figures show that nearly one-fourth of the communes of France (8,381 out of 37,510) contained no one who even spoke French; more than 10 percent of all French schoolchildren spoke no French, and a remarkable 48.2 percent of schoolchildren age seven to thirteen could not write in French. The persistence of regional languages and local patois underscores the variation of subcultures.

https://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/popular-and-elite-culture