Loubert says it is a Damask (Vibert 1843)
I doubt (as Vintage does) that the rose in commerce is a Hybrid Perpetual:
"This has been offered for some years by Heirloom Old Garden roses, and we are surprised they have not noticed it doesn't rebloom at all. It is in fact a Damask rose, not the Hybrid Perpetual, Mme. A. Labbley. Flowers are small, very double, deep rose pink with a lovely fragrance. Grows like Leda."