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”.