Very nice and exciting quest!
-as already said, you can purchase IGN's maps. The best for this kind of searching is "Série Bleue France" in 1/25.000 scale. The map you need must be n° 2308 O
(I can check it better in a bookseller/ stationer's shop). You can order it in the IGN website (or I can do it if you want ;) )
If you go back to the area, it will be very easy to find this map in a good stationer's shop in Amiens.
But this kind of map will only show you actual roads, not fifties roads (sometimes, "ancient circuit automobile" is written on them, as it is in Rheims' section).
Anyway, the best for your quest is to be on the place and go the town hall of the city/village you think the track was and ask to see the land registrer ("le cadastre", in french). They must have plenty of old maps with sharp scale, sometimes 200 years old ! Checking them is free of charge, but sometimes it's not possible to check them, because in some touristic places, too many people asked to see the maps to know who is the owner of a plot they want to buy. Anyway, explain your request and I'm sure you will have no problem.
If you don't find something in this village, you can also ask in Amiens to the Departmentals Archives (hope the writing is correct, sorry for my poor english...)
I'm living in Bordeaux, so too far to go tomorrow in Amiens (
), but I will spend some days in Paris until the end of the month. Perhaps I can go to Amiens if you need it...;)