I searched the internet but found nothing
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I am posting this as a comment as the information is incomplete. There are several pieces of vintage art work (circa 1920's) listing the Onyx brand bicycle. The posters all have French text which would lead you to believe it is a French brand. The oddity is your head badge is in English There is also an identical head badge listed on Etsy . It is listed as a vintage head badge from the 1980's.– mikesMay 28, 2018 at 21:37
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Unfortunately, "Onyx" appears to be a widely-used brand (probably licensed out by the brand owner), so there's no central repository of info, and no way to link the relative quality of the disparate components.– Daniel R HicksMay 29, 2018 at 1:07
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2I believe it's ORYX, the animal and not ONYX, the mineral. Googling ORYX cycles gives some exotic results.– MikeMay 29, 2018 at 14:30
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1Now the goat like animal on the head badge makes sense!– mikesMay 29, 2018 at 20:28