Why did France try to suppress regional languages/push for cultural hegemony in France, especially during the 19th century?

I mean the simplest answer is that those things began to happen as a result of the French Revolution and the Napoleonic Wars. Before the Napoleonic Wars the modern concept of nationalism did not really exist, there were tons of regional languages and vast cultural differences with little to anchor the citizens of France to the country as a whole. France was very segmented and people identified themselves by their region or even town rather than call themselves "French"--that concept just didn't exist. It was the realization that wars cannot be won without nationalism that led to huge pushes from all European nations to become more cohesive by not only establishing a single language, but also establishing national symbols to forge a united culture. If you read diaries from the Napoleonic Wars like the "diary of Friederich Ludwig Burk" you will see the lack of nationalism. Friederich was highly concerned about the citizens of his town and his home, but he barely mentions the larger war being fought outside of his community. It is pretty hard to win a war if your citizens feel no connection to it and you have to hire mercenaries who don't speak the language and really, really have no ties to the war being fought. As a side note, when studying wars the issue of language comes up a lot-- its important for the effectiveness and safety of soldiers for units and their supervisors to speak the same language so everyone knows whats even going on. This European trend that you are describing can, in part, be blamed for the severity of WWI as by that time people, comparatively, were highly nationalistic.