Trying to identify movement from dimensions?

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I found this watch in my parts drawer and can't remember where it came from.
The obvious answer is that I'm looking for a Valjoux 88. But the height of the space inside the case is about 3.8 mm and the Valjoux is 6.9 mm high.
I suppose it is probable that someone has put this dial in the case and coincidentally the dial fits perfectly?
The company whose name is on the dial was one of the top Jewelers in Paris and I'm wondering whether that company would have made or sold a watch in this cheap nickel looking material with a stainless steel back? I also don't know whether they would have been forced to compromise their standards during wartime?
Does anybody recognize the positioning of the pushers on either side of the case and have any idea which movement went in such a case and would have fit the dial at 29.5mm please?



Again, it could well be that the name on the dial is just a distraction and the movement I'm looking for is the chrono movement that Eska would have used with these four pushers