'Baby Faurax' cannot be bred by Léonard Lille, as he died in 1913 at the age of 82. Candidates for the breeder are his son Louis Lille, or the latter's son-in-law Joseph Faurax-Lille, who married Jeanne Lille in 1917 and took over the Léonard Lille grain business by 1921. The rose 'Mme Faurax-Lille' would have been dedicated to Jean Lille, the roses 'Elisabeth Faurax' and 'Louis Faurax' probably to children of the pair. 'Baby Faurax' would have been either Elisabeth or Louis.

In it's second year now and it has exploded in blooms.
Just random observations.
There was a minor to bad bout of powdery mildew (primarily around flower buds), but no other health issues so far.
Every flower seems to set a hip, the hips only have 1 or 2 seeds each....getting the seeds out of the tiny hips is a little tricky. Seeds germinate fairly well.

My 2018 just-for-fun crop of ‘Baby Faurax’ seeds were picked on March 10 from a tiny plant growing almost underneath ‘Hermosa’. Close by is ‘Orleans Rose’ and ‘Mrs. Alston’s Rose’ but I am conscious that a bee can fly a long way even when laden down with pollen. They were placed intact in the crisper and on April 22 they were shelled and planted into potting mix. By August 8 I had pricked out 20 little babies. Two died and I am left with 18. 16 are repeat flowering of which:
2 are red - one is an attractive double, and one is an incurved single (not so good)
3 are whitish or very pale pink and all are awful, almost malformed.
11 are all about the same dark pink, so much so that I resorted to names like Huey, Dewie and Louie for some. Most of them are attractive double blooms and one ‘Wink Blink’ reminds me strongly of ‘Veilchenblau’ blooms.
2 did not flower but have made stronger and longer growth with one cane up to 2 metres. Does this mean these two (‘Whipper Snapper’ and ‘Jack’) are going to be spring flowering only climbers?