In the video below, Data refers to the French language as "obscure". Picard objects to this and Data is about to make a remark as to why the French language was indeed obscure. Is there any indication given in any other materials as to why Data considered French to be an obscure language?
I keep going back to the Writers Guide again and again, as well as in this case. The description of Jean-Luc Picard states among other things:
Born in Paris, France, Picard betrays a gallic accent only when deep emotions are triggered. Otherwise, since ethnic accents are no longer common, he carries only a touch of French phrasing in his speech. In discussions with friends, he pretends to believe that France represents "the only true civilization" to appear on Earth -- and that it delights him when a witty companion wants to prove the same for England, Italy or China. He is definitely a 'romantic' and sincerely believes in concepts like honor and duty although on issues that affect the safety if his crew and starship he can be completely pragmatic and tough as hell.
"Federation Standard" is the common tongue for Starfleet and Data, who not only know this and French but also a huge range of other languages, presumably classify languages with fewer then N users to be obscure. If we take the first definition of obscure from Merriam Webster:
- not well-known : not known to most people
it is fair to assume this is a direct cold fact way of presenting it from Data's fact-ridden way of thinking.
When it comes to the particular clip it is clear that they intended it to be a humorous awkward moment precisely because of Picards love of France. This is further underlined by the reaction of the crew. A situation we all know; when someone unknowingly is stepping on someone else's toes ;)
This isn't a great answer, but it's fairly heavily hinted throughout the "modern" series (TNG, DS9, Voyager) that the official language of the Earth is standardized English, and that other languages are basically of hobbyist and research type use only, the way Latin is today. There is also more than one reference of inferior cultures that don't have a common language, and that is one indicator of them being inferior.
As for why French was used specifically, it may be for a light comedic moment with Picard. Or for the reasons of being one of the most widely spoken languages (geographically) in the world, mainly competing with English for geographic spread.
French is also the language other than English that business is conducted in at the UN. Other languages were added as additional working languages later. Some committees and offices in the UN only use English and French to this day (Per Wikipedia). Also CERN requires most staff to speak, write, and read both.
While Picard states that French was the dominate international language, it has been in decline as English has become the defacto standard since World War 2. Wikipedia
Once the key international language in Europe, being the language of diplomacy from the 17th to mid-20th centuries, French lost most of its international significance to English in the 20th century, especially after World War II, with the rise of the United States as a dominant global superpower. A watershed was when the Treaty of Versailles, ending World War I, was written in both French and English. A small but increasing number of large multinational firms headquartered in France are using English as their working language even in their French operations, and to gain international recognition, French scientists often publish their work in English.
With the center of Starfleet being located in San Francisco, you can imagine it has an English-centric influence on the planet. Additionally, which Africa has been growing in use of French in the last few decades, we don't know what affect World War 3 and the forming of the African Confederation (or the United States of Africa) had on their continued use of French.
Based on Data's statement, we can assume that by the 24th century, French has become a niche language.