Of course people walk their dogs. Must people who live in cities in continental Europe (where in some places it can easily reach 38/40° in summer, 36 in Toulouse next week for example) don't have a garden, so dogs still need to be walked.
However, for the same reason they don't have a garden, it's easier to find shade. Buildings are often 5/6 floors high, streets are narrower (often there are no parking spots on either side of the street), just enough room for pavement on each side and single lane trafic.
People are also less fussed about exercising their dogs. A gentle stroll 3 times a day is generally considered decent exercise. There are plenty of smells, other dogs, noises, any sort of stimulations...less green spaces though. And rarely off lead time. But they're not unhappy. It's just different standards and habits.
It's also controversial but in Europe its very common to work all day and the dogs hold their bladder from the morning till the evening, which makes a walk at midday less frequent.
Now, even at 7pm, its still boiling hot, and those tall buildings made of old stone don't lose much heat at night so it's also very hot indoors. Not a lot of flats are equipped with AC because well, old buildings not built with AC in mind. You won't find an AC unit in an Haussman building unless it's a hotel.
I do agree though that there's a glorification of exercise here, which I tend to agree with 90% of the time, I find it marvellous to see my dog running off lead every day and I take pride in giving him 2h a day, but dog ownership isn't only about having a tired dog.
I had a corgi in Paris, wonderful little chap, he had a dog walker during the day when I was working but it was mostly for company, quite often she would just sit in a café with my dog and partake with Parisians' favourite activity of watching people. not doing anything. He was out for 2h a day but probably didn't have more than 40 mins of walking in total.
In London I now have a tiny little terrier, by all account what should be a sort of lapdog, but because he got used to run everyday, i may get away with 24h of quiet toilet breaks round the block but after that he'll be driving me crazy. He just got used to much higher standards. Good for me that despite being a british breed, he's adapted to that weather (but anything below 12° and he needs a jumper)
I don't buy the acclimatisation argument. Cities like Toulouse can be freezing cold on Monday and boiling hot by Sunday. Its as brutal as it is in the UK. My french friend whatsapp group is talking about that right now. "Blablabla I had a coat on monday and now I want to rip my skin off blablabla"
To conclude this long essay, the difference is that people WALK their dogs but they don't necessarily exercise them.