Welcome to the boards, Magnifico!
Cafe's are littered everywhere in Paris and Madrid. I´ve been to many of them and just chilled. In fact, there are so many that it´s hard to remember their names! You just kinda cafe hop here and there.
I remember there were some chilllable ones in the Latin Quarter and Monmarte area in Paris. Also, by the Champs Elysse.
In Madrid, there are a ton too! There is one that I frequented called Cafe La Palma (metro/ San Bernardo). Cool chill vibe in the afternoons and later in the night they do stuff like poetry readings and dj´s. There are districts like Santa Ana and streets like Fuencarral that have many cafes with relaxing atmos.
Here´s a list of some cafe's and clubs in Madrid
I´ll let you know more if anything pops in the head B)