When it comes to non U.S. and U.K. productions, the rules have to be a bit different. I think only specific research on a title by title basis is useful.
Bob le flambeur, for instance, I can assure you all is framed at 1.37:1, despite the time it was made. One scene I just checked is early on and takes place in a bar. Bob is sat at a table, with the camera filming him face on. The camera pulls back in preparation for him rising, and as he does so his head reaches the top of the 1.37:1 frame and remains there for a few moments as he addresses a companion, still sat down.
If you crop this scene, the pull becomes pointless, as Bob's head rises out of frame regardless and for a few moments he addresses his companion whilst cut off at the nose. There are a few other examples like this, and I found them after a less than 5 minute flick through of my Criterion DVD. The whole film cropped even to 1.66:1 I don't think could be bearable (assuming the Criterion transfer isn't heavily zoomed, though we don't have a reason to think it is).
Whether it's Indian, Japanese, or more "western" film making from France, the same rules just don't seem to apply. Both Godard and Tati have made it clear they made many of their post-widescreen era films in 1.37:1, in some cases using non-anamorphic widescreen on some pictures and then going back to 1.37:1. It seems like it was a whole different ball game over there.