In 17-18th century France, how common was it to beat your servants up, such as mentioned in French theater?

Yes, there's poor Master Jacques, in Moliere's The Miser, who keeps getting beaten by different people for different reasons....hard to laugh at it now.

A servant was part of a household, ruled by the master and mistress of the house. Slaps, kicks, scolding and other real or verbal abuse was just a part of the normal interactions of that pre-industrial world . A servant girl who dropped and broke a cup could be slapped, a farm hand who was found sleeping in the hay he was supposed to be raking could be kicked awake. But this is also a harder world, where food was quite expensive and bread was often put under lock and key, and where slaps and kicks and punches were thrown around far more generally ( consider how often Don Quixote is beaten...and we're to laugh). And the master and mistresses own children could expect slaps and kicks from them, as well.

There is a very strong element of class in this: servants had to take beatings from their masters, they could not beat them in turn. When the Chevalier do Rohan felt insulted by Voltaire, he sent his servants to beat him the philosophe and they did so, but they were acting as the men of the Chevalier and Voltaire was of a lower class. Voltaire was unable to demand the satisfaction of a duel from the chevalier. Had the Chevalier insulted or struck another count, of course there could have been a duel.

Allowance for abuse did not extend to outright murder. The Newgate Bloody Register has some cases of servants murdered by their masters/mistresses, who were then hanged. ( In 17th-18th c. France there were I think some more notorious cases of nobility getting away with murder...I will dig out the specifics and add them later)

/r/AskHistorians Thread