A café crème is espresso with hot milk, served in a 150 to 200 ml cup. Despite the name there is no cream in it — crème here describes the colour and the texture.
Where it sits
Between an Italian cappuccino and a latte. More milk than a noisette, less than a latte, with a light foam rather than a thick cap.
It is the standard French order for anyone who wants milk in their coffee and does not want a tiny cup. In Paris it is usually just called un crème.
The Swiss usage
In German-speaking Switzerland, Kaffee Crème means something different again: a long black coffee, closer to a lungo or an americano, with no milk at all. Cream may be offered alongside.
The same words, two unrelated drinks, four hundred kilometres apart.
Making one
A double espresso in a 180 ml cup, topped with around 100 ml of steamed milk with a light foam. Less foam than a cappuccino, less milk than a latte.
The other French orders
Un café is an espresso. Un allongé is lengthened with water. Un noisette is an espresso with a dash of milk. Un déca is decaf.
Ordering “a coffee” in France gets you a small strong espresso, which surprises a lot of visitors.