An American asking for a coffee in a French cafe receives a small cup with a couple of mouthfuls in it. That is the standard order, not a mistake.
The default word means espresso
Asking for a cafe returns a single espresso, because that is the unmarked form of the drink in France and everything else is described by an additional word.
An American-style long coffee has to be requested specifically, and it is made by lengthening an espresso with hot water rather than by brewing a pot.
Filter coffee kept warm on a burner, the standard in American diners, is largely absent, so there is no large-format default to fall back on.
The drink is a pause, not a companion
A counter espresso is consumed in a minute or two, which fits a habit of stopping briefly several times a day rather than carrying a cup around.
Refills do not exist as a concept, because each cup is a separate priced item rather than a serving from a shared pot.
That is also why to-go cups are less common outside tourist areas and major stations, though they have spread in recent years.
Milk drinks are tied to the time of day
A large milky coffee is a breakfast drink, and ordering one after a meal is noticeably unusual, though nobody will refuse to serve it.
The version served after lunch or dinner is an espresso with a small amount of milk, which is a different and much smaller drink.
Understanding that distinction avoids the common outcome of ordering by translation and receiving something twice the expected size or half of it.
Price follows the cup, not the volume
Because coffee is priced per cup, a larger drink costs more without containing proportionally more coffee, since it is mostly added water or milk.
The cheapest option is nearly always the plain espresso taken standing at the counter, which is the tier locals use.
Water is served alongside on request without charge, and taking it is normal rather than a special demand.
Quality varies more than size does
Ordinary cafes serve coffee as a functional accompaniment to a seat, and the quality is often unremarkable even in expensive locations.
Independent roasters have grown in French cities over the last decade, and those places serve the range an American specialty shop would recognize.
The two coexist without overlapping much, so a traveler chasing good coffee should look for the specialist shops rather than expecting the traditional cafe to deliver it. The traditional cafe is selling a seat and a street view, and the coffee is incidental to that.
Specialty shops also tend to keep shorter hours and close earlier than cafes, which means the good coffee and the long evening terrace are rarely available in the same place at the same time.