My portable A/C unit recirculates the inside air through the evaporator coil until it hits a temperature set point, then it cycles the compressor to hold it there. A separate fan blows air over the condenser coil to pull out the heat; it is that heated air which is exhausted to the outside.
However, I've experienced permanent air conditioning as executed by many places in France. I don't think they really grasp the concept, at least in many of the hotels. Either that or they don't want to spend the money to beef up the electrical grid in Paris and other cities to handle the added load (I assume they have enough generating capacity, with all those nuke plants).
That is the way portable units work, and they do work, but obviously you cannot continuously expel air without making it up in some matter. When the condenser is outdoors, then you’re not expelling any inside air to cool the condenser.
As to the hotels in Europe - I’m convinced they’re under orders to limit how low their air conditioners can be set. Pretty stupid since soon their only ‘product’ will be tourism, thanks to them self de-industrializing by both listening to the Neocons and listening to the Globalists.