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There's a website called Le Bipede which lists races in France.
Being able to understand a bif of French will help, as there is no English translation.
Look under 'Calendrier des courses' and put in the month, department, distance, etc., to find races.
To race in France you will need a medical certificate - or letter from your doctor - stating you are fit to run a race. Some races will now accept a UKA Competition LIcence, if you have one.
There is also a site called Topchrono.biz , but they're slow to put the events until the last minute, almost. Another is jesuiusuncoureur.com