There is no such language in France.
I think we need to take a step back:
Why is French perceived as "fancy" or "classy"?
From the Wikipedia History of French: Modern French article:
From the 17th to the 19th centuries, France was the leading power of Europe; thanks to this, together with the influence of the Enlightenment, French was the lingua franca of educated Europe, especially with regards to the arts, literature, and diplomacy; monarchs like Frederick II of Prussia and Catherine the Great of Russia could both not just speak and write in French, but in most excellent French. The Russian, German and Scandinavian Courts spoke French as their main or official language, regarding their national languages as the language of the peasants.
I think that this is where the idea that French is the language of elite sprang from: French was used by the nobility, scientists, artists... everybody that was somebody.
It is also interesting that, as remarked in comments, English itself promotes French as a fancy language.
In 1066 William the Conqueror, then Duke of Normandy, gained his title by conquering England. He installed his fellow Normans as the nobles of England.
This means that much like above, from then on French was the language of the nobility and high class. In turn, it means that even in modern English, French retains a special place, and French borrowed words are generally perceived as more refined than their Anglo-Saxon counterparts.
Since then, English has thoroughly overtaken French in terms of number of speakers; but in doing so it has also promoted French as a fancy language.
Also notable, you can find a "Lycée français" (literally, French highschool) in many countries. Generally, they are frequented by the children of French diplomats or expatriates, but also, and crucially, by some of the children of the highest class of the country in which they are.
These schools not only promote French, but also reflect positively on French and France as they give excellent education1 to their (elite) students, further reinforcing that France and Excellence go hand in hand.
1 Excellent ~French~ education, with French history and culture having a pro-eminent place.
More generally, this extends to French culture. Considering its relatively small size (~70 millions inhabitants only), France has a disproportionate influence in the Luxury market (restaurants, fashion, ...) and in arts (Festival International du Film de Cannes, for example). The French Riviera is a prized destination, with Monaco just nearby, ...
All this contributes to France having a dream-like quality.
The only language which achieved such status in France was Latin, which was spoken by the nobility and clergy. However, during the French Revolution (1789), the nobility and clergy lost some of their shine to say the least.
And even then, Latin had been losing ground for some time. The French Academy was established by Richelieu in 1634, Rabelais was publishing books in French in the 16th century.
The only current language that has such a widespread use as French is English, however France and England have been at odds for a long time (you may have heard of the Hundred's Years War). Recognizing that English is "better" than French is thus unlikely, it would be conceding victory somehow.