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Meaning
Please forgive my swearing.
Origin
A coy phrase used when someone who has used a swear-word attempts to pass it off as French. The coyness comes from the fact the both the speaker and listener are of course both well aware the swear-word is indeed English.
This is mid 20th century English in origin. A version of it is found in Michael Harrison's All Trees were Green, 1936:
"A bloody sight better (pardon the French!) than most."
The precise phrase comes just a few years later in S.P.E. Tract IV., 1940:
"Excuse my French! (forgive me my strong language)."