How do they “not worry about rent”? The local franchise pays rent to the parent company.
I don't have any specific insight into the EU, but in the other global markets I'm familiar with (mostly China, Hong Kong, Singapore, and Japan) locations are either owned by McDonald's directly or franchised by large corporations that have significant bargaining power with (and sometimes are) landlords.
The China/HK franchise, for example, is operated by CITIC (a Chinese SOE) and Carlyle.
"The company owns about 45% of the land and 70% of the buildings at their 36,000+ locations (the rest is leased)."[1]
This article is from 2015, but I don't have any info that disputes it.
[1]https://blog.wallstreetsurvivor.com/2015/10/08/mcdonalds-bey...