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I don't think a good history of the Armée de l'Air in 1939-1940 or of the air battle in May-June 1940 exists now.
All books I know are interested mainly in only one airforce.
As for the French airforce, some books show victories (Gillet) while others show losses (Martin), few will describe operations, especially bombing and recon ones.
The greatest failure of Armée de l'Air IMOO was its failure to affect the ground battle. Bombers had almost nil influence and each unit was almost decimated in the first sorties. Fighters were unable to protect the troops from German bombers and Stukas (that were more efficient and used at the right places in great numbers), mostly due to doctrine of use.
Martin's book "Ils étaient là" lists all air losses of operationnal units of Armée de l'Air, not operationnal losses. Planes of second lines unit (local defence flights, for example) that get shot down are not shown, while planes of first line units lost in training, ferry and so on are.
It also doesn't cover the Aéronavale (French Fleet Air Arm).
No published source lists the French ground losses AFAIK. Armée de l'Air was never crushed on the ground but several units were decimated and retired to the rear to be recompleted. Most of the times they returned with more modern planes but so some units were missing on the frontline for some time.
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