What is the smallest city in your country that everyone can still instantly recognise the name of? What is it famous for?
In the United States, I'd probably name Oregon City, the famous end of the Oregon Trail and the first city founded west of the Rocky Mountains during the pioneer era. Its population is only 37,000.
For France it's probably Vichy, infamously well known internationally for being the capital of the French pro-Nazi government during the Occupation. Only 25'000 inhabitants.
Admittedly my WW2 history knowledge is quite lacking, but I don't recognise Vichy because of the war stuff.
But I do recognise Vichy! Because we have a sub-type of mineral water in Sweden that is named after Vichy, "Vichyvatten". Wikipedia tells me the original was from a spring near Vichy, hence the name.
Even without considering cheese villages (somebody mentioned Roquefort, I was thinking of Gruyere, France clocking in at about 100 inhabitants), I believe Verdun would be just as known and is smaller at a population of around 17000.