It was built by J. Rossel & Fils (brothers) who was the successor of J.F. Bautte. The J.Rossel & Fils brand was used from 1883 to 1897. Then the business was acquired by Felipe Hecht and in 1906 sold to Girard Perregaux.
Eri, are you sure that the Rossel et Fils brand only began being used in 1883? I ask because I have a keywind Rossel et Fils free-sprung pivot detent chronometer that looks to be a pre-1883 watch. See https://mb.nawcc.org/threads/swiss-kw-detent-chronometer.147257/. The Schmitt auction house listed it as having been made in 1860. Because the watch appears to have been aimed at the notoriously conservative English market, I suppose it could have been made in 1883 or later if you are sure about the 1883 date.
At the beginning it was Rossel-Bautte et Fils in 1844 factory in Rue de Rhone 62, then it changed to Rossel Bautte & Cie from 1860 to 1883 always in Rue de Rhone 62. From 1883 to 1897 J. Rossel et Fils factory in Rue de Rhone 12 during this period two third category prizes at the Geneve Concours de Chronomètrie and a first prize the following year.
This company name was in use from 1883 to 1897 Rossel & Fils, Succ'r de J.F Bautte & Cie, Geneva
and from 1897 becomes Felipe Hecht successor of J Rossel Fils ancient maison JF Bautte.
Note that the JF Bautte brand is still by Girard Perregaux.
Enrico, thank you so much for this information! It's really fascinating and I'm sure my dad will be interested. I'm a bit shocked at the age of it, considering it's in such lovely shape still! My grandmother must have treasured it.