Definitely not thornless and the leaves don't look very HP unless the plant is from late in the era when some were as much china as damask. The flowers look HP but to my nose they have a very strong lemon scent which suggests china or other influence. I have never known a citrus-scented HP.
Has this been compared to 'Empereur du Maroc'? Or perhaps 'Souvenir d'Alphonse Lavallee'?
For the second suggestion, be aware that some photos in that HMF file are 'Erinnerung an Brod', and some maybe even 'Souvenir du Dr. Jamain'. SdDJ differs most noticeably in that it is less fully double (with stamens showing in the center) and "more thornless" if not completely so. EaB seems a more obvious distinction -- look for the Setigera leaves.
We had a true Alphonse in Australia until a couple of years ago (at Ruston's); there may still be stock plants around, but the two nurseries here offering it have effectively closed. See helpmefind.com/rose/l.php?l=21.65187
Looks like the photo transfer glitch is still active. Transferred photos appear on the description page for the rose, but not under the Photos tab for that rose.