If you are on a roll, talking fast, and suddenly you spit out a profane word or two, then you say it: Pardon my French.
But why do you say that last bit?
According to the Cambridge Dictionary, you said that because you were pretending to be sorry for using offensive language.
That started around the 1830s, when every educated person spoke French, but the people they were talking to usually didn't. So they would beg pardon for speaking French. That was especially true after the Napoleonic Wars left England and France at odds.
But the phrase quickly evolved to its current use, which is a fake apology for anything profane, according to Grammarist.
