The French certainly benefitted from the earlier Jesuit work, although the French did do their own attempts at “westernizing” parts of the language. I understand that today in Vietnam, the main train station in Hanoi is called “Ga Hà Nộ”, where “ga” comes from the French “gare”, meaning train station (eg Gare du Nord in Paris). This kinda makes sense since the French would have been around when railways were introduced in the 19th Century.

Another example is what is referred to in English as the “Gulf of Tonkin incident”, referring to the waters off the coast of north Vietnam. Here, Tonkin comes from the French transliteration of Đông Kinh (東京), which literally means “eastern capital”.

So far as I’m aware, English nor French don’t use the name Tonkin (it’s very colonialism-coded), and modern Vietnamese calls those waters by a different name anyway. There’s also another problem: that name is already in-use by something else, being the Tokyo metropolis in Japan.

In Japanese, Tokyo is written as 東京 (eastern capital) in reference to it being east of the cultural and historical seat of the Japanese Emperor in Kyoto (京都, meaning “capital metropolis”). Although most Vietnamese speakers would just say “Tokyo” to refer to the city in Japan, if someone did say “Đông Kinh”, people are more likely to think of Tokyo (or have no clue) than to think of an old bit of French colonial history. These sorts of homophones exist between the CJKV languages all the time.

And to wrap up the fun fact, if Tokyo is the most well-known “eastern capital” when considering the characters in the CJKV language s, we also have the northern capital (北京, Beijing, or formerly “Peking”) and the southern capital (南京, Nanjing). There is no real consensus on where the “western capital” is.

Vietnamese speakers will in-fact say Bắc Kinh when referring to the Chinese capital city, and I’m not totally sure why it’s an exception like that. Then again, some newspapers will also print the capital city of the USA as Hoa Thịnh Đốn (華盛頓) rather than “Washington, DC”, because that’s how the Chinese wrote it down first, and then brought to Vietnamese, and then changed to the modern script. To be abundantly clear, it shouldn’t be surprising to have a progression from something like “Wa-shing-ton” to "hua-shen-dun’ to “hoa-thinh-don”.