Look for a number or logo under or near the escapement and balance wheel.

The day is probably set by turning crown round and round till the right one shows. Date is probably set by moving the crown in and out. It's an early quick set design.

 

I can just barely see the edge of the logo under the balance wheel there. Looks like the ETA logo.

 

Okay, that's very helpful - I see what I believe is "2638" written under the balance wheel, which Google suggests is an ETA number, although I know nothing about it.
Is there any way to tell which of the assorted quality levels ETA tend to make watches to this is (if that's applicable) this might be, or even when it might have been made?
Also if anyone can point me at any documents on the movement I'd appreciate it. (I found this but don't have a logon: https://www.cousinsuk.com/account/login?ReturnUrl=/PDF/categories/2011_eta+2620+.pdf )

 

P.S. I haven't worked out how the quickset works - there is no working second click out for the crown. You can advance the date by going back and forth between 8 and 12 and a bit and repeating. The day advance seems semi-random and I can't work out how to change between French and whatever other option it might have?

 

Your watch may not have day in a second language. For example my Omega Seamaster from 1970 has only German. Try just pushing the crown in and out repeatedly to see if that frees up the date setting mechanism.

 

bidfun-db Archive: Watch Movements: ETA 2638

 

A 2638 is supposed to have date quickset, but there was a time when oscillating back and forth between 8PM and midnight was considered to be quickset.

Try gently pulling the stem out past the winding detent to see if there is a spring-loaded position that changes the date. That was one scheme, but I don't remember if ETA ever did it.

This watch dates from the late 60's or very early 70's.

The day wheel will often support English and French. When it advances, it goes two positions, passing the unused language. But it often does so slowly and there many be a period after midnight what it shows the second language. Just advance the hands (during the day) until it shows the correct day. The quickset will not change the day display.

Rick "who hates setting day-date watches" Denney