In France if you order, “un café, s’il vous plaît” (a cup of coffee, please), the waiter will bring you a café noir or café express, a small espresso-sized cup containing a few spoonfuls of dark, very strong espresso coffee. On the saucer will be a few cubes of sugar and perhaps a chocolate and/or a lemon rind wedge, none of which should you touch if wish to be taken as French.
If you want weaker, American-style coffee, and hence a bigger cup of it, find a place offering café filter, which is not offered in most self-respecting establishments and will mark you as outsider.
At breakfast, many Parisians prefer café au lait (also called café crème), which is an espresso served with hot milk in a larger cup. From mid-morning through the afternoon, you might prefer a cappuccino, espresso coffee and steam-foamed milk with a sprinkle of cinnamon, or powdered or shaved chocolate, atop the foam.
You can order any sort of coffee déca or décaféiné (also called faux—fake) which is decaffinated, also marking you as a non-hexagonal sort.
Only at breakfast will the cafe come at the same time as food, for with lunch or dinner, your coffee until after you have finished your meal and dessert, and is never taken with milk.