Thank you Patricia for answering so quickly !
I've been looking at the Rubaiyat rose page, the first picutre was so remiding me of the location of the rose ! But the Rubaiyat blooms look much fuller ! There is a picture of Ensalada from Vibert that looks like it, but it is a 2001 rose.
My dear great-grandmother, who strongly contributed to my interest in gardens, passed away more than twenty years ago. My mother owns the house today but the garden is "à l'abandon". I went there and took several cuttings this year so I will probably try to identify them with the help of the Helpmefind community !
I think the only clues are in my memories. First, the house and the garden were built in the late 1950s, and a great attention was given to the lanscape.Everything was meticulously chosen, located and taken care of.I have seen documents were the choice of trees were discussed with the lanscaper but they didn't mention the roses. I think my mamie must have selected them herself, and she must have used some cuttings.There were some famous efficient roses like Centenaire De Lourdes, there is also an own-root Superstar/Tropicana that comes from her at my parents' house.But I think this rose is older and I heard that the cuttings were given to her by one of her cousins, and I remember it had a special status.
I am surprised that I didn't see it appear in the books I read or in the tremendous Helpmefind list of roses ; apart from the fragrance which I still have to check with my cuttings, it has some qualities, like surviving under a fir tree, having a good lanscaping presence. There is also something "artistic" about the flower, I think, it is reminding me of Georgia O'Keeffe. I am not an expert, but it being reliable, eye-catching, slightly-scented, I would have expected it to be a success of its time, like the aforementioned roses.
Patricia I thank you so much for sharing your time and knowledge, I've been searching so much on Helpmefind since I dicovered it, and I have read a lot of your comments/looked at your pictures.
Have a nice day, protect yourself, Thomas.

I took new pictures of that rose last month. I am getting lost in my searches, but maybe I should investigate further about Tiergartendirekor Timm. Lafayette is also a name that frequently comes back. Here are some more informations :
-12 to 15 petals.
-purple new stems and leaves, leaves sometimes bordered with purple, especially on young cuttings.
-hairy pedicels.
-actually it can grow higher than 1.50m.
-round hips, found on one similar shrub isolated from the bedding.
-very neat, pointed buds.
-small clusters.
-the wave is subtle, much less tight than Permanent Wave.
Thank you, Thomas.

After doing some research I think this rose could be Cyclamen 1959. The Roseraie du Val De Marne website describes it as a tall bush (they do grow it). They have a picture of it where one can see the slightly red-bordered leaves, whose shine is also similar. 1959 makes the timing very short, as the house and garden, including the bed were these roses were planted, were built in the late 1950s. This makes me wonder if they are actually own-roots, but could a grafted rose have survived for so long ?