For anybody who might want to know:
I have found a place to rent skates. At
Aubert Sport in Rue de la Pontaise you can rent skates for periods varying from half a day to a month. It cost me CHF 38 to rent skates for 10 days and the protection is included in the price. I thought that the service in the store was very nice.
Note: on the website, it doesn't say that they rent skates in the 'location' section, but they do.