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Thanks very much for sharing this excellent find!
Shall look forward to following along as you work forward with it.
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From your researches you probably know that Rene's racing career covered the years 1932-1939.
His Silver Medal at the Los Angeles Olympics of 1932 was for team pursuit.
Following one of his racing victories he reported that the machine he rode was constructed by his brother Louis.
The brothers opened their store in November of 1937.
He passed in 1946 at the age of thirty-five.
Some French collector & history experts report that the production cycles which bear his name were done by Mercier. Others do not agree. There is one report that his widow entered into a joint agreement with Mercier to produce cycles with the Le Greves name.
Le Greves badged machines were manufactured until the late 1960's.
fr.wikipedia.org
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Your example -
The stem is Philippe model Nr. 35.
Pedals appear they may be Brampton (of France). Here is an advert from 1926.
Have you found any markings on the inner faces of the crankarms?
Markings on bottom bracket fittings?
Chainwheel appears to show a painted coating; you may wish to consider removal to see what lies beneath. Does it have any markings on its backside?
Machine's chainguard appears to have gone walkabout. See images posted below to view an original.
You asked for information on the cycle's Juy Champion du Monde rear mech. There is some here:
This Simplex Champion de Monde Extra-Leger is an example of a design that Simplex produced in a lavish range of different variants and under a profusion of different names (Champion 35, Champion 36 and Champion de France being some possibilities) between 1935 and 1948. These derailleurs were a...
www.disraeligears.co.uk
What make are the bicycle's brake calipers; CLB perhaps?
Is gear block a Moyne?
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Here is a Le Greves
berceau which appears it may be close in time to your machine -
Porteur of 1950 -
Fifties era juvenile -
Late production road model showing Mercier origin -
Ringer -
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