• Belle de Woodlands
• Noisette à fleurs rouges
• Noisette rose à petite fleur
• Noisette rouge
• Pourpre (noisette, Laffay, 1822)
• Pourprée (noisette)
• Purpurea (noisette, Laffay, 1822)
• Red Noisette (noisette, Laffay, 1822)
• Rosa noisettiana purpurea
• Rosa X noisettiana staxon purpurea Redouté & Thory

10 favorite votes.  

Bred by Jean Laffay (France, 1822).
Introduced in France by Jean Laffay in before 1824 as 'Purpurea'.
Introduced in United Kingdom by Exotic Nursery (England) / Joseph Knight in 1825 as 'Red Noisette'.
Introduced in Australia by Camden Park in 1843 as 'Purpurea'.

Noisette.  

Violet-red or mauve, ages to darker . [Light purple.]  Small, double (17-25 petals), very double, cluster-flowered bloom form.  Rounded buds.  

Armed with thorns / prickles, climbing.  Small, wavy or ruffled foliage.  

Rosa x noisettiana staxon purpurea Redouté & Thory. Roses 3:103 (1823)

There are probably at least two roses by the name of 'Red Noisette'—see References. The wavy-leaf rose referred to by Andrews is, he writes, not a Noisette...if it was imported from America by Philippe Noisette to his brother, Louis Noisette, the last name could be the source of the confusion.