Strange conversation going on.
Yes,
European cities have trees.
And yes,
European cities have parks within walking distance.
In The Guardian link that started this whole conversation, you can clearly see parks and trees in even the densest square kilometers, and more just outside.
A lot of this conversation seems to be centred on Barcelona, for some reason. I'd guess because it has the densest square kilometer. First, 53k in a square kilometer is crazy dense. The Gothic Quarter is an insane labyrinth of tight lanes but, like Leo pointed out, you don't need shade. When it does open up into squares, the squares have trees,
like so. If you want a green break, Ciutadella Park is directly to the west. The Mediterranean and white sandy beaches are less than a kilometer from the southern edge. And at the northern edge there are multiple metro lines that will take you to the mountains 5km to the north.
The history of Barcelona's Gothic Quarter is really interesting. Barcelona backed the losers in the War of Spanish Succession, in 1714. Spain, therefore, forbid the city from growing beyond its walls. For the next 140 years, Barcelona became increasingly dense. By the 1850s it was something like the 19th century Kowloon Walled City. The Gothic Quarter, as roughly half of the old city, had an incredible population density of about 85k per square kilometer.
In 1854, Spain lifted the restrictions on Barcelona's growth. Barcelonans ripped down the city walls, converted the citadel to the west--built to oppress them--into a beautiful park, and expanded the city into Cerdá's Eixample--the expanse of iconic square street grid with chamfered corners.
So, that's why the Gothic Quarter is extremely dense and lacks space for a lot of street trees or large parks.
And I now hear that their (fake) lack of trees means European cities are dealing with the heat poorly. Are European cities dealing with the heat poorly? I don't know. There's less air conditioning than in NA. More of life goes on outdoors, in public spaces. I shouldn't need to explain why hiding from heat in air conditioned cars doesn't mean Canadian cities are handling global warming.
European cities are tuned to their traditional climates. This means that southern European cities--which tend to be built closer together, to create more shade, and that therefore tend to have fewer street trees--are already equipped to deal with the heat. Climate change is more of a problem in Northern Europe, where cities were built to maximize light during dingy winters.
Northern European spaciousness, though, leaves more room for trees, which already exist, and more of which cities are planting.
Seville, handling the heat like the always have.
Amsterdam, planting trees to deal with the unbearable sun and heat characteristic of North Sea cities. 
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If they really demanded trees, they’d be having them, through the sacrifice of some other characteristic. It’s not like trees can’t grow at Paris’ latitude.
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