Standard Parisian coffee is a small black espresso (un café). Cappuccinos and lattes are for tourists at most cafes.
A café crème is a milky coffee for breakfast. Don't order a cappuccino after 11 AM unless you want a confused glance.
Third-wave coffee shops (Coutume, Ten Belles, KB Café Shop) serve modern espresso, flat whites, and pour-overs.