Why are the French pejoratively referred to as frogs?

According to the French newspaper Le Figaro, the reason has to do with a neighborhood across from Paris called La Grenouillère:

MY TRANSLATION:

La Grenouillère or more precisely La Guernouillère [low river marsh where frogs congregate] for the natives who lived along the river was a small hamlet on the [then] "outskirts" of Paris, facing the Tuileries Gardens, which became known in the 18th century for the high quality of its washerwomen and laundresses who carried out their labors by "the weight" or "item of clothing". These hamlet dwellers spoke what was certainly a lowly patois, which the upper classes of the time found comical. The "language of la Grenouillère" became a symbol of the naive good nature and the liberties of speech of the Parisian lower orders.

This manner of speech gained visibility in the 1750's through Jean-Joseph. Vadé's famous Letters from the Grenouillère, which later gave way to numerous imitations. This "Parisian patois" was very useful in particular at the time of the 1789 Revolution, when some of the pamphlets penned by aristocrats used it as a didactic weapon against the foul-mouthed Louis Jacob Hébert in his rag Le Père Deschenes.

Be that as it may, in 1790-1791, not only those living in La Grenouillère but also, by assimilation, all the people of Paris were being called "the frogs" by the court nobility....Undoubtedly, this generalization reflected the influence of Aristophanes' play The Frogs on educated aristocrats. The action takes place mythologically on the banks of another famous river: the Styx! In short, at the Court of Versailles in 1791, the opinion of Parisians, the humor that reigned among activists in the capital, could be summed up in the oft-heard question, "What do the frogs have to say about this?"

With this phrase in tow the most realistic of these aforementioned privileged persons escaped abroad. In the face of human anger, absolute pessimism is a must; this was borne out many times in the 19th century and Rohmer's film The Duke and the Englishwoman recently illustrated the need for fleeing.

Thus, the most clairvoyant of these nobles ended up in London where their émigré community spread the term "Frogs" throughout the English aristocracy. These very ravaging frogs that continued to grow bigger than cattle and soon more predatory than wolves,[...]

[The article goes on to say to say that the revolution was forgotten but that the epithet remained.....]

• The article is by Claude Duneton, "Writer, actor and staunch defender of the French language....sorry, I could not do the rest of the article, but the bit I translated shows it main point.....one wonders why the OED did not pick up on any of this.....

The last line of the article is: La morale de ma chanson est qu'on n'est jamais si bien nommé que par soi-même!

The moral of my song is that best name is the name we give ourselves.

the real story of froggies

/// TRANSLATION: In France, during the Revolution, the frog, which was rare compared to other animals such as the cat, dog, pig, ass, chicken or turkey was thus more used by the counter-revolutionaries than by the patriots.

En France, durant la Révolution, la grenouille, rare par rapport à d’autres animaux comme le chat, le chien, le cochon, l’âne, la poule ou le dindon, est donc davantage utilisée par les contre-révolutionnaires que par les patriotes.

Ah, Curséd Animals

Below is a painting by Alexandre-Jean Noël of the place known as la Grenoullière, on the left bank of the Seine, facing the Tuileries Quay

The OED says we’re not completely sure, but it may in part have started as a reference to the wet and marshy Low Countries and then later reïnforced by the shared initial consonant cluster between frog and France/French:

With sense A. 8 (in use with reference to persons or individuals) compare early use as a byname and surname: Nicholas Frog’ (1207), William le Frogge (1275), William Frogge (1332), etc. The precise reasons for the specific uses in senses A. 9 and A. 10 are uncertain; in A. 9 perhaps with allusion to the marshy and low-lying nature of the Low Countries (compare later Froglander n., frogland n.); in A. 10 perhaps with allusion to the supposed popularity among French people of frogs’ legs as a dish, and perhaps partly also on account of the shared initial consonant cluster in frog n.1 and French adj.; however, both senses could simply show narrowing of sense A. 8 to identify the inhabitants of countries which were near neighbours and frequent rivals of Britain.

Sense A. 8 is the general one for people as a term of abuse, sense A. 9 is an obsolete derogatory one for the Dutch and other folks from the Low Countries, and sense A. 10 is specifically a derogatory term for the French, one which is often capitalized.

III. Extended uses applied colloq. to persons and their speech.

8. A person likened to a frog. Usually as a term of abuse.

9. † derogatory. A Dutch person; = Froglander n. Obs.

10. Usually derogatory. Frequently with capital initial.

    • a. A French person or a person of French descent; occasionally as a form of address.

    • b. The French language.

The earliest citation for sense 10a is from 1657:

• 1657 Sir W. D'Avenant First Days Entertainm. Rutland-House 55
  Your Kitchins are well lin'd with Beef;..whilst those in the Continent..entertain flesh as a Regalio; and we, your poor French Frogs, are fain to sing to a Salade.

The earliest citation for sense 9 is five years earlier in 1652. The sense 8 citations are older than both of those, which is why it’s sense 8: the OED lists senses in historical order.

Grammarphobia cites Brewer’s Dictionary which suggests the frog-eater assumption, but also the French fleur-de-lis heraldic figure which was sometimes described as three toads saluting:

According to the Oxford English Dictionary, the word “frogs” has been used as a term of abuse for men and women since the 14th century. During the 17th century, it was used to refer to the Jesuits and the Dutch.

Brewer’s Dictionary of Phrase and Fable traces the use of the word “frogs” for the French to both the eating of frogs’ legs and the fleur-de-lis, the French heraldic device, which was sometimes described as three frogs or toads saluting. In the 16th century, Nostradamus, alluding to the fleur-de-lis, used the word “toads” for Frenchmen, according to Brewer’s. In the late 18th century, the dictionary says, the French court routinely called the people of Paris grenouilles, or frogs.

In the late 18th and early 19th centuries, according to the Random House Historical Dictionary of American Slang, “frogs” and “frog-eaters” began showing up in English as derogatory terms for the French people.

The site The Symbolism of frogs and toads suggests that the link between the French and frogs/toads has ancient and simbolic origins:

It’s a surprisingly twisted tale that starts a solid millennium-plus ago with the Frankish King Clovis. Uniting the regions that would later constitute France, Clovis converted to Christianity around 500 C.E. on the heels of a victorious battle. Legend suggests a hermit appeared to Clovis bearing God’s message: that he should swap his family’s heraldic shield—three sable (or black) toads standing erect—for the Christian (and now iconically French) fleur-de-lis, whose three stylized leaves could be read to symbolize the Holy Trinity. Nothing punches up the drama of a conversion like a king ditching a frankly evil shield for a purely noble one.

But how did heraldic toads get mixed up with an insulting nickname for the French? Enter Nostradamus. In Seward’s Anecdotes, we find:

• When the French took the city of Aras from the Spaniards under Louis XIV it was remembered that Nostradamus had said: ‘Les anciens crapauds prendront Sara’—the ancient toads shall Sara take. This prophecy of Nostradamus (he died in 1566) was applied to this event in a somewhat roundabout manner. Sara is Aras backward. By the ancient toads were meant the French, as that name formerly had for its armorial bearings three of those odious reptiles instead of three fleur-de-lis which it now bears.

Nice answer by @tchrist. I add this as more interesting and 'out there' information:

'In the course of researching this I came across a few odd ball suggestions and here is one. ‘ When the French laugh, their adam’s apples bulge out of their necks like frogs.’

'It is possible that Nostrodamus was the first person to refer to the French in amphibious terms.'

From poitoucharentesinphotos.wordpress.com