Maillard sprocket: is really this rare?
If the Shimano freewheel didn't fit, it means that your bike uses French threading for the freewheel (which isn't surprising given that it has a Maillard freewheel; the other non-bmx standards are interchangable). You're basically out of luck and need a new wheel (or at least new hub). 

Depending on the hub, you may have to re-space the frame(*), since 6 speed likely means 126 mm rear spacing, where a newer hub would be 130 or 135 mm. This isn't difficult, and a shop that has a decent amount of clients with older bikes should be able to do this easily. You can also still find 126 mm wheels on the market if you look (Velo Orange still sells them, for example), so you wouldn't need to respace the frame. Or, you can respace it yourself. But this is the way I'd go. 

(*) Assuming its steel, which given the age, it probably is.