It's rare to get more than a couple of days of temperatures over 30 C in the summer here in northern France. The big canicule (heat wave) was back in 2002, I think - but since then the summers have actually been rather cooler than normal. Air conditioning is expensive (due to the energy costs involved) and only really needed for perhaps 5 days a year. Floor units are surprisingly large, but I suppose you could get your own. The big question is how you are going to vent the unit (usually require taking out a pane of glass in one of the windows - something the landlord may or may not want you doing).Pardon my North American sensibility and ignorance but I have to know 2 things...
1. Why do unfurnished apartments in Paris typically not have air conditioning? Is buying your own floor unit for example allowed if one can't be places in the window? I know the temperatures aren't supposed to get very high, but for a few years now we've heard about temperatures in the high 30s (celsius) in Paris, haven't we?
Have you looked at most windows in flats and houses here? Normally, the windows open into the room from the near side of the wall. You could conceivably put a screen on the outside part of the wall (say, just behind the shutters), but with stone walls particularly, there is no place to build in a "track" to hold the screen.2. Is there really no way whatsoever to put screens in windows? I make my own here in the states with screening materials from hardware stores. But I have two cats, and I'd rather that they weren't tempted to take off or have anything happen to them while observing pigeons!
A couple years ago there was the attempt to market screening material here in France. I was sorely tempted, but wasn't sure how I was going to secure the screens in the window spaces (still allowing for a "balcony" for the cats to sit and enjoy the evening breezes). Evidently I was about the only person even to consider this because the screening material has all but vanished from the market. (It is still available if you search for it - but you would have to determine what you would need to make it work in the windows where you are living.)