Bravo Laurent, bravo Peter. Peter's views, I think, are even more accurate and close to reality. Congratulations. May I add that not only France but also the Netherlands and Belgium, both being small countries but modern, well-equipped and well-armed, and having brave armies, and also the cream of the British Army were beaten too, or even worse than the French. Even if France had possessed an air force which would have been PERFECT (for the time, 1940) in every respect including numbers, Germany would have won because of its particular, very clever but very risky strategy (Ardennes, Sedan, race to the coast etc.) and because of the incredibly incompetent, stupid and slow-reacting top Allied commanders (French AND British). 1940 no country was in a position to win a big war thanks to its air force alone and it is doubtful even of 1944-45 - the western Allies and the USSR all engaged great quantities of tanks, artillery and... infantry. They certainly had good reasons to do so instead of relying on their huge air forces alone.

As for books there are many - in French, in English and in German. This question was discussed here some months ago : you should be able to find it - and the titles of many books - using a few well-chosen key-words : French Air Force, 1940 + books, French Campaign, 1940 air war etc., both here at TOCH and on the general Internet (Google, Yahoo).

In my eyes - this is only my opinion! - the best allround-book on this is :
"Air War over France 1939-40", by Robert Jackson, published 1974 by Ian Allan Ltd, Shepperton, Surrey, England. ISBN 0 7110 0510 9
It should be possible to find it, for ex. on the Internet. It has only 154 pages of normal size (about 1/2 A4) and deals with virtually everything : bombers, recce, fighters etc., Allied night bomber operations, all countries involved in the fighting including the Netherlands and Belgium, and even the French local fighter units at Bourges, Châteauroux, Lyon etc. and the French naval aviation! This really is quite an achievement! Statistics, general results, description of the main aircraft etc. Of course you can't expect a detailed account of ALL operations and of every single air battle with the complete list of losses and victories, but this work is excellent indeed. There are a few errors, but they don't matter much : for ex., "Orléans in Southern France" (this city is in Central France, on the river Loire) or famous ace Werner Mölders shot down on 14 May (top of page 112) instead of 5 June.
A highly recommended book!

There are only two French allround-books I know of. They are much bigger and both were researched and written mainly by Paul Martin : "Invisibles vainqueurs" (1991, normal book size) (title invented by his publisher Yves Michelet, who added more "optimistic" pages and photos, totalling 50 % of the contents, to Martin's dire hundreds of French aircraft shot down and dead aircrew [almost nothing on the German losses except tables of French fighter victories (with AC types shot down and French units) in the annexes and their number for every day, in the main text, in a few short words]) and "Ils étaient là..." (2001), an enormous book in large format, mainly a 2nd edition of the preceding book, Y. Michelet's comments and views being replaced by new publisher C-J Ehrengardt's (Aéro Editions publishing company, Fleurance, France) and author P. Martin having added numerous French aircraft losses (and probably human losses too), for ex. 11.43 % for Morane 406s and 56.25 % for Dewoitine D.520s. The photos are mostly not the same ones as in the 1st edition. Martin's books are a precious source of data mainly on French aircrew and aircraft losses of all types (bombers etc.) (which are described in detail whenever possible) and also on French fighter victories but readers who are not well-informed before reading this get a very sad, pessimistic impression of permanent, heavy French losses which does not correspond reality for both sides suffered heavy losses fighting each other, the German losses being higher, in particular in bombers.

There are many more specialised French books (monographs etc.), many of them still available at least as second-hand copies : D.520, Curtiss H.75, French bombers ("LeO 45, Amiot 350 et autres B4"), and others, in the "Collection Docavia" of Editions Larivière (look in the magazine "Le Fana de l'Aviation for their publicity) and also excellent books published by Lela-Presse (magazine "avions") : MS 406, Bloch 152, Potez 174, Les Curtiss (français ; published 2008). Don't forget the excellent review "Icare" with 19 big issues devoted to the 1940 French Campaign 1970-2007 : Chasse, Bombardement, Reconnaissance, Bombardement d'assaut etc. The mentioned books all report war operations and individual air battles with units, losses and victories.

The best allround FRENCH book is probably a Docavia : L'aviation de chasse française 1918-1940, published 1972 (but still excellent) by the remarkable experts Jean Cuny and Raymond Danel. It deals mainly with the fighters but gives a good general idea of the whole story and precious tables and statistics (like : 912 modern French fighters in first-line (combat) units on 10 May 1940 - did you know that? - plus about 50 in local flights and 35 with the Naval aviation, the grand total being about 1,000 French fighters in combat units, but only 2/3 were supposed to fly, 1/3 being reserve aircraft which proved very useful, leaving approx. 670 "active" fighters on the front and also all over France for the factories and cities had to be protected against bombers). This book is out of print (épuisé) but you can find it, on the Internet too.

Most books can be found in libraries (French : bibliothèques !) and they exchange books if some of them can't be found otherwise.

Good luck!