Surely a Sachs or an ILO 98 would do that? There were names like New Map and Ydral in France, and hundred of Italians. I'd personally love a Motobecane "velomoteur leger".
I live 4 miles, 6-7km, from the National Motorcycle Museum. I've been to the Sammy Miller Museum in New Milton, it's a few miles from Southampton if you get a boat across, or a bit further from Bournemouth if you fly there. There are autojumbles throughout the summer across the country, and there are events like Founders Day for the VMCC.
The NACC,National Autocycle Club have branches and runs, and are a very good source of information and contacts.
We have lots of aircraft museums (I am upset, Elvington has a helicopter my age, and it's obsolete
, so it would be possible to travel only a few miles at a time from one place to the next.