Judging by these Gaumont films ascribed to Alice Guy from 1906 and 1907, crosscutting was increasingly becoming common practice around this time, although employment of the technique tends to be brief, as it is here. But, the film is only comprised of five shots, so everything about it is brief. Continuity across shots is fluid, as well, and follows the axis of action. The falling through the floors bit is especially well done. Otherwise, "The Cleaning Man" is a mess of knockabout slapstick, where the titular cleaning man ends up destroying what were already flimsy sets by Gaumont.
In other films from Guy accessible today, crosscutting also appears in "The Drunken Mattress," "The Truth Behind the Ape-Man" (both 1906), "The Glue," "A Four-Year-Old Heroine" and "The Irresistible Piano" (all 1907), as well as perhaps in others.
By the way, I love fellow IMDb reviewer Martin Hafer's comments regarding "frotteurism" as a psychological term for a "compulsion by perverts to brush up against strangers," as that adds an entirely new perspective to "Le Frotteur"--how he runs into the maid and everyone else upon the slippery floor. It would explain a lot, actually.