granville1 said:
“However, I've never heard that it was supposed to be the aunt herself who was possessing Robbie.”
As GRANVILLE1 mentioned above, “La Plume De Ma Tante” is a non-sequitur comment made by the demon inside Regan. JGUTHRIE is also right, “La Plume De Ma Tante” is one of the very first phrase you learn in French class. And no, that comment by Regan has nothing to do with little Robbie and his aunt.
William Friedkin mentioned that in that particular scene Regan knew the intentions of father Karras. She knew he was trying to find a sign of possession by speaking in a language that Regan could not possibly know. Thats why Pazuzu decided to have a little fun with father Karras by mocking him and speaking in foreign tongues just for the hell of it. But ultimately, father Karras is the one who had the last laugh when he sprinkled Regan with supposedly holy water. 