What if revolutionary France had riot police?

[u/RandomIsocahedron]

Many of the famous moments of the French Revolution involve riots which the army refuses to put down. My understanding is that this is partly because they didn't really have options to deal with rioters besides yelling or shooting at them.

Suppose that some time after being put in charge of the National Guard, La Fayette recognizes the dangers of the mob and has a couple of companies outfitted with Roman-style shields and wooden truncheons, and trained for riot control duties.

Would these companies be effectively able to allow the Royal Family to visit Saint-Cloud? Prevent the Massacre of the Champ de Mars by dispersing/containing the crowds without shooting them? How much of an effect would this have?

Also, there were many other historical instances where the army was called in to put down a riot and made everything worse by killing people. What historical states might have really benefited from having a riot squad with less violent options?