The MAS 38 was the Waldo of French weaponry. Every time I find one in a photograph (which is not very often) I go "Woah! I've found a MAS 38!" Since only about 2,000 were made before the defeat, they were not issued in any regular fashion to any particular unit. In general, you could find them more commonly among corps francs, the ski scouts of the chasseurs alpins, officers, and the GRM.
German MP38s were much more common, although I'm not sure when the design changes for the MP40 designation had been implemented.
I don't think the British Mk. 5 mine was around in 1940.