Use
 

There are few clues to find the origin of this expression, however, at least one source allows us to affirm that the expression has derived and changed meaning. In the 19th century, when English-speaking people used expressions derived from French, they apologized, probably because their interlocutor was not comfortable with the French language. This definition cites as an example its use in The Lady’s Magazine in 1830, to forgive the use of the word “embonpoint” (overweight). However, the term was already used at the end of the 19th century to avoid the use of coarse words. Still today, the expression is used rather before uttering insults.
 

The expression known today has been democratized through television programs, and in films intended for a family audience, in which words that were not offensive were preceded by "pardon my French" to intensify their effect without violating the rules of censorship, and avoid using words that might shock. It is also a demonstration of French bashing suggesting that the French spend their time swearing.
 

Related Expressions
 

Moreover, several expressions are used by both the English and the French to describe behaviors that are not seen culturally speaking, and to attribute it to another community, such as "filer à l'anglaise", which also exists in English: "to take French leave".

Originally, real French words were placed in conversations. French was until the Versailles Accords in 1918, the language of international agreements, usually spoken by educated people.

One of the earliest occurrences in an 1830 magazine was “The Lady’s Magazine, or Entertaining Companion for the Fair Sex, Appropriated Solely to Their Use and Amusement”:

Bless me, how fat you are grown! Absolutely as round as a ball. You will soon be as overweight (excuse my French) as your poor dear father, the major.”

The example speaks for itself.

Then this frankly snobby attitude became a way to drown out one’s own vulgarity under the pretext of using -without doing so- foreign words.

Perhaps the perception of the French as a people of dirty pedants and letting their cheese rot while copulating has helped popularize the use of this expression in that sense.

Today, it has become a common expression, used without any ulterior motives.