I'm not sure about this rose; is it the Gallica, also known as Roi de Rome, or is it the Hybrid Pepetual Enfant de France. I also have the rose Spencer (also of doubtful lineage), and that one looks exactly the same as my Enfant de France. The rose only blooms once a year and is slightly susceptive of mildew later in the year. The rose Enfant de France was sold as a Hybrid Pepetual, but I am not so sure any more about that.
If there is an occasional repeat, then it is probably the HP, if it is once-blooming, then the Gallica. Although in these strange times, even Gallicas are sometimes having scattered blooms in autumn.
I don't know how helpful this will be, but I saw Enfant de France some years ago at the Huntington when the rose was blooming. The scent had an element that I dislike--whether this is myrrh or musk, I'm not sure, but some of the David Austin roses also have the same element in their perfume. Mary Rose is an example of whatever that smell is that both roses have in common. Now Enfant de France at the Huntington was, as I recall then, a fairly compact plant with a narrow vase-like shape. Flowers were light pink.
Last year at Eurdodesert in the hybrid perpetual beds I saw the rose Spencer. It was quite big and tall. I didn't sniff any of the flowers so can't comment on the fragrance, but the flowers looked larger and darker pink than I remember on Huntington's Enfant de France. I don't know about rebloom, but Cliff Orent would know whether his rebloomed or not. He could be asked where he got his plant too. I have a picture of the Eurodesert Spencer somewhere or other on my computer. I'll look and post if I can find it. Also I probably have one of the Huntington's Enfant de France, but it is likely in print form stored in a box. However, others may have readily available images of it which they could post. The comparison would be interesting.
Hi Tessie/Melissa, thanks for your information and photo; this one look somewhat different from the roses that I have. The blooms are brighter pink and the smell is more rose-like en not the myrrh scent (which by the way I like very much). What I think is very unusual, are the bright red stems on new leaves in July, both on my Spencer and my Enfant de France. I will add a Photo of the leaves.