I have just read the above phrase again today while reading a newspaper article. It is not the first time and I have always presumed to understand it well. I did observe the use of obscene words before or after the phrase is said.
Although correct with my observation, I don't know the reason involving the French. I did a Google search as to the origin of the phrase and found several interesting answers, all related.
Here is the answer I chose (source: Yahoo Answers), which seems to me sums up the best description as to the origin of the phrase:
This phrase, in which French refers to "bad language", is employed when the speaker feels compelled to use an obscenity despite having listeners who might be offended. It's a late 19th century euphemism which first appeared in Harper's Magazine in 1895.
It is thought that the term French is employed in this sense as it
already had a history of association with things considered vulgar.
As far back as the early 16th century, French pox and the French disease were synonyms for genital herpes, and French-sick was another term for syphillis. The OED [Oxford English Dictionary] also equates the adjective French with "spiciness", as in French letter for "condom", French kiss (1923) and French (i.e. "sexually explicit") novels (from 1749).