|“||Even my incredibly long life is too short for Les Miserables.||”|
— The Doctor
French came about some time before 1572. French was spoken by the mob of bloodthirsty lunatics who killed a bunch of people on St. Bartholomew's Day. Later, Madame de Pompadour and her cuck husband spoke French, in between having sex with aliens and horses. Mickey Smith was, at this time (sorta), visibly horrified to discover that the TARDIS was making him speak French.
Sometime after that, French was spoken during the Reign of Terror. When given the choice of going to the guillotine or surviving and hearing more people speak French, Susan Foreman decided to give up her head.
Vincent Van Goff, noted madman and drunk, spoke French with a Scottish (which is to say, Dutch) accent. The French people who surrounded him eventually lead to his shocking and horrible murder, which was quickly covered up as a suicide. Not realizing he had in fact been murdered, the Eleventh Doctor and Amy Pond both happily visited the Musée d'Orsay, where the French kept the trophies they'd taken from the murdered, tortured, and canonically most wonderful genius who had ever lived.
Further down the line, French was spoken by a brutish policeman who accompanied the Fourth Doctor and Romana around the City Of Death: Paris. In addition, a French-speaking alien was eager to murder not only every Parisian, but indeed the entire human race by inventing time travel. The French detective (that's a pretty good name for a detective story, btw) mercilessly beat him to within an inch of his life, thus ironically saving the very world that every French person desires to destroy.
After the Doctor exterminated his own species, he himself became infected with the terrible memetic virus that French truly is. The ninth and tenth Doctors both exhibited symptoms of the terrible malady. In one instance, an otherwise normal woman speaking French was enough to justify a stewardess sacrificing her life to throw the woman out of an airlock.
Behind the Scenes
"French" is allegedly based on an obscure branch of the romance family, spoken exclusively by subhuman beasts that shamble about in dark, frightful places or icy wildernesses. No actual hard evidence exists for the existence of French in reality, and most people who claim to be able to speak it are conclusively found to just be mumbling gibberish.
In an unfilmed scene set immediately after the Eleventh Doctor's regeneration into the Twelfth, Twelve claims to have deleted French from his mind. As this scene was never filmed, its canonicity remains dubious.
Quotes and Media
"It's useless! Nul points!" ~ The Doctor, informing the Daleks he plans to exterminate all life on Earth before they arrive.
ROSE: "And on the other side of the magic door is France in 1727?"
DOCTOR: "Well, she was speaking French. Right period French, too."
MICKEY: "She was speaking English, I heard her."
ROSE: "That's the Tardis. Translates for you."
MICKEY: "Even French?"
~ Shocking revelations
"Allons-y!" ~ The Doctor, shortly before murdering someone or fleeing justice.
"You've got everything I need for an omelette fines herbes, pour deux." ~ The Doctor, preparing to poison his roommate Craig.