First, this is very difficult to answer in general: such things depend widely on the person speaking, its usual language and adequation to context. Regarding expressions that cover the same type of usage as “pardon my French”, I would translate it as:

• passez-moi l’expression
• si vous me permettez l’expression
• excusez mon langage

But those are not really specific to profanity, while “pardon my French” is mostly used when uttering curses. They can be used to excuse familiar language in a formal context, such as a business meeting.

In italian we ironically ask someone who said something vulgar

Hai studiato ad Oxford?

That is

Did you study at Oxford (university)?

Implying Oxford is a very good school. On the other hand the English expression is quite an anachronism, since nowadays you can hear profanity almost everywhere in France, even on public television

There’s no equivalent I can think of. Spontaneously, I’d say “Pardonnez-moi l’expression”, but there’s no way to, as you say, “pass the blame”.

But there’s something in the same vein: somebody that doesn’t understand a very complicated jargon can say “Pour moi, c’est du chinois”. That’s the French equivalent of “That’s Greek to me”. Less employed but still existing: “C’est du javanais”.