1934 Ford 3 Window Coupe ever see military use?

Not sure.  Maybe not part of the fleet "Officially" but I imagine so somewhere!

I'm just spitballing here, but I imagine anything with four tires ,and. A motor  found it's way to europe

Try one of the pre-WW2 conflicts.  I've seen photos of cars impressed into service during the Spanish Civil War.  Use it as a pilot hack picking up/dropping off pilots of Polikarpovs.  Or how about a AVG P-40 in China or one commandeered by Japanese to fuel up Ki-27s at Nomonhan?  Find an ad hoc or  haphazard situation where normal military organization isn't available.  This should allow you to weather it up as well.  Just make sure you don't put it in a country that had right-hand drive.

Jack

A three window coupe staff car? I highly doubt you could stuff a general officer in the back seat of a three window coupe. A fodor (sic) sedan is more likely. That having been said, be creative and use your imagination. During  WWII all sorts of vehicles got pulled into military use.