As late as 1870, nearly half the population of rural France did not speak French or identify as "French." They identified by their region or village (Breton, Occitan, Basque, Provençal). The Third Republic used the Jules Ferry laws of the 1880s to enforce mandatory, secular public education (banning regional languages in schools under threat of punishment) to forcibly mold a disparate rural population into a unified French nation.
Other than the Bretons and Basques, all of these people spoke the same branch of gallo-romance dialects, which was in a continuum with Parisian French.There was no such thing as a separate Bourbonais or Berrinchon people, just Frenchmen under the rule of the duke of Bourbon or count of Berry, neither of which existed anymore.