It's not an answer to your question but could be a practical solution to your problem: Street parking, where allowed, is free from 19:00 to 09:00. You will only be staying a couple of hours at each end of this time period so you can simply pay a few euros when arriving to bridge the time until 19:00 and pay again before going to bed for the two hours in the morning. In total, you would pay much less than €30. I did just that a few months ago and it went fine. I think you will need a credit card.
If you are able to find a parking spot (this might be the difficult part) and you are not concerned about the safety of the area, there is no reason to go to a car park overnight. I have also heard that some streets are still completely free but parking is not that expensive and relatively unrestricted compared to other European cities so it never seemed worth the trouble.
Some official info in English: parisinfo.com
Paris.fr also provides some info, unfortunately only in French as far as I can tell. What you would be using is the “tarif visiteur”:
Le tarif visiteur
Il s’applique à tout visiteur sur l’ensemble des voies parisiennes ouvertes au stationnement payant, ainsi qu’à tout titulaire d’une carte de stationnement résidentiel sur les voies de régime rotatif ou en dehors des 4 zones de stationnement résidentiel qui lui ont été attribuées.
Le stationnement au tarif visiteur est limité à deux heures consécutives au même emplacement.
Translation/summary of the relevant bits: The visitor price applies to all streets opened to paid parking. […] Parking as a visitor is limited to two hours on the same spot.