Mopeds, Cyclemotors, BMA, Autocycles, Bicycle Attachments...
'Motor-bicycle' was the original name for motorcycles, and is appropriate for the first models which were precisely that, ie strengthened cycle frames with engines. The term 'autocycle' was sometimes used for 'motorcycle' (hence ACU - Auto Cycle Union). But that subsequently became the name for a class of pedal-operated single or two-speed machine under 100cc with limited speed (around 20mph). These were in use from 1931 until the 1950s as a result of a tax concession in UK, Germany & France. That concession was then lowered to under 50cc in UK. After WW2 the term 'cyclemotor' is applied to bicycles with engines attached. Around 1953 the word 'mo-ped' was coined, and they took over from cyclemotors.
The USA doesn't have much history of similar early machines so 'motorised bicycle' has become a generic term to describe everything. I sold this 119cc Evans Powercycle a few years ago. It was one of the few US contributions to the genre, made by the 'Cyclemotor Corporation'.
~ Colin Kirsch, via Motorcycles 1867-1930 FB Group.
Mopeds in France
Towards the end of the 1970s mopeds had achieved great popularity. Motobecane and Peugeot were the largest manufacturers and they benefitted greatly when the French government banned sales of geared mopeds with the issue of decree N°80-14 of January 1980. Many smaller marques vanished within a year or two unless they could produce models with automatic transmission.