How can I find a way to climb on a rooftop in Paris and just to chill out there?

One great budget option in Paris is the rooftop cafe at the Galerie Lafayette.

From there, you’ll be able to see the Opéra Garnier, the Eiffel Tower, Sacré Cœur, and Notre Dame. In addition, you’ll be able to see the Galerie Lafayette’s famous stained glass dome.

It’s free to go up there and it’s fairly affordable to purchase coffee or wine at the rooftop cafe.

It’s open from 10am to 8pm, and the sunset is beautiful from there.

Here’s a new one in a converted post office in the 2nd arrondissement :
https://parissecret.com/paris-nouveau-rooftop-roof-poste-du-louvre/

This one is situated on top of the former prefecture de paris in the 4th arrondissement and will be open shortly :
https://parissecret.com/bonnie-rooftop-paris/

In the 3rd arrondissement this is a roofop bar in the Arts et Metiers area:
https://www.hotelnational.paris/fr/pagex/rooftop-bar-paris.137.html

This is a rare rooftop bar/restaurant in the 11th arrondissement which I can recommend because of its beautiful views from the east side of the city
https://leperchoir.fr/location/le-perchoir-menilmontant/

(I’m not associated with these businesses)

Probably pure luck, friendliness, confidence, and courtesy. You have to be in the right place or know/meet the right people. Some locals may have access that the general public will not. I’ve stayed at AirBnBs in Manhattan, Mallorca, Venice, just outside of Rome, and the 5th arrondissement of Paris with private, rooftop access for just our unit. In the case of Mallorca, the roof access overlooked both the city and the palace.

In the case of Venice, it just happened to be an attic storage area that was converted into an apartment. It was not an official hotel room. We would not have been allowed to stay there except that our original accommodations had been uninhabitable due to a maintenance issue. And, the rest of the hotel (as well as other hotels in the area) were all booked solid.

Several options:

1. From the roof of the Arc de Triomphe the view is fantastic, in particular the Eiffel tower, a fee is needed for the visit of the arc.

2. Less central, the terrace on top of the Institut du monde arabe offers a very nice view of the Seine & Notre Dame, free access.

3. From the Tour Montparnasse there is a nice view, the big advantage is that you don’t see the tower. Entrance fee.

I think your best bet will be to befriend locals.
As it is not easy to meet the right people by accident, you can try the online meeting places.

I would personally start with any members of any groups I am already part of who happen to live in Paris, but that depends on being part of an international or French organization. If you are not (yet) you may look if your hobby has regional or local groups with online presence, as you will have your hobby to talk about (rather than just begging access to their roofs.)
Next are the sites that are specially made for meeting people, couch surfing among others, and sites where people who travel hang out, (I am told the Lonely Planet site has one that actually works.)
Introduce yourself, tell them that you will be in Paris in a while, would like to catch the sun on a Paris roof and do they know someone with access to a Paris roof?

You have to realize that there are not that many roofs available. My Paris friend who lives in a top floor apartment may or may not have access to the actual roof, (I was there in March and April, not the time to sit out on the roof.)
His flat is on the top of 6 more floors of apartments and non of those has roof access, as only the top floor has that if any.
It is even rather likely that most roofs in Paris are not made for access and that many of the people who you see on those roofs are there (semi) illegal. If there are no railings, they are not legal to use, just like flat roofs lower down without railings are not for sitting or walking on. And while people are willing to take the risk for themselves, they are less likely to share with strangers and even less when asked online by strangers (who may be building inspectors or something like that.)

So while I think it is not impossible to get on a private roof, I would not expect you to find it easily.

Renting an apartment (airbnb or other) in the roofspace may work, even better if it is advertised with ‘roof access’.

There are a few touristy locations which have roofs that can be accessed. I remember being on the roof of the Basilique du Sacré-Cœur, as part of a ‘see the building’ route, for which you pay an entry fee. One of the views is on the photo. You do not walk on the actual roof nor can you stay out there in the sun for a long time, but you can have a good look.

Photo taken by Willeke, 5 April 2015. (I place this photo in the public domain now.)

Not all big buildings in Paris have roof access tours but some more may have.