I know it's so Last Century but you can do this with actual hardware.
After a bit of experimenting with alternatives I've decided you can't beat the Michelin atlas as a starting point. Then get some round coloured sticky things. I bought mine from a local stationer but you can get them on line. The ones I've got are about 5 mm in diameter.
Then mark your route on the atlas with the stickers. I don't use many, three or four a page usually but that's enough to show the general direction to head.
I was surprised to find that my ancient copy of Microsoft Autoroute works on Windows 10 on my P.C. without a problem. It does just what you want and you can print out the resulting route (or individual bits).
Yes it's getting on a bit but *if* you could find a copy (discontinued in 2013!) it gives you the ability to type in a list of towns, then at the touch of a button shows where they are on the map. Then it will let you plot them in optimal order. And if you want you can drag the route marker and drop it in another spot.
I think mine's from 2005 but there cannot be many towns that were not about then or many that no longer exist. Mabe a very small number of changes to the occasional road layout but nothing to change an overall route.